Sample records for d3h symmetry zigzag

We report a measurement of a new high spin Jp = 5- state at 22.4(0.2) MeV in 12C which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D_3hsymmetry characterized by the sequence 0+, 2+, 3-, 4+/-, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D_3hsymmetry was observed in triatomic molecules and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1-) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular the observation (or non-observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha-particle composing the Hoyle state at 7.654 MeV in 12C.

The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the alpha-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle with D(3h) symmetry for 12C, and a tetrahedron with T(d) symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.

A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts rotation-vibration structure with rotational band of an oblate equilateral triangular symmetric spinning top with a D3hsymmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our measured new 2+ 2 in 12C allows the first study of rotation-vibration structure in 12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D3hsymmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of 12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in 12 C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in 12C. We discuss proposed research programs at the Darmstadt S-DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.

Using density functional theory combined with nonequilibrium Green's function formalism, we investigate the transport properties of zigzag graphene nanoribbons (ZGNRs) under vertical strain. Our calculations show that localized state induced by vertical strain will inhibit the electronic transport of the systems at zero bias, but at nonzero bias, the localized state can enhance the electronic transport behavior if ZGNRs are symmetry with respect to the mid-plane between two edges. This is because the localized state produces an asymmetry electron density distribution which break the current suppression. These findings may be useful for the application of strain-induced ZGNR based molecular devices.

Full Text Available We performed the first-principles calculations to investigate the spin-dependent electronic transport properties of zigzag-edged germanium nanoribbons (ZGeNRs. We choose of ZGeNRs with odd and even widths of 5 and 6, and the symmetry-dependent transport properties have been found, although the σ mirror plane is absent in ZGeNRs. Furthermore, even-N and odd-N ZGeNRs have very different current-voltage relationships. We find that the even 6-ZGeNR shows a dual spin-filter effect in antiparallel (AP magnetism configuration, but the odd 5-ZGeNR behaves as conventional conductors with linear current-voltage dependence. It is found that when the two electrodes are in parallel configuration, the 6-ZGeNR system is in a low resistance state, while it can switch to a much higher resistance state when the electrodes are in AP configuration, and the magnetoresistance of 270% can be observed.

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.

The first use of the flexible Schiff base ligand N-salicylidene-2-aminocyclohexanol in metal cluster chemistry has afforded a new family of Ln7 clusters with ideal D(3h) point group symmetry and metal-centered trigonal prismatic topology; solid-state and solution studies revealed SMM and photoluminescence behaviors.

Using the canonical force field theory, expressions of quadratic, cubic, and quartic canonical force constants are obtained for XY3 (D3h) molecules in curvilinear redundant coordinates, i.e., simple valence internal coordinates (VICs), in terms of force constants in normal coordinates and in independent symmetry coordinates. To carry out this task, it was previously necessary to obtain for the first time the non-linear redundancy relation and the corresponding orthogonal projection onto the pure vibrational manifold for XY3 (D3h) molecules corresponding to a set of seven VICs. As an application, the quartic canonical force field in curvilinear redundant internal coordinates of BH3 is determined from ab initio force fields in normal coordinates calculated at the coupled-cluster singles and doubles level with perturbative treatment of the triples in conjunction with a triple- and quadruple-ζ size basis set. This anharmonic force field so obtained for the borane molecule, and in general for XY3 (D3h) molecules, is uniquely defined (therefore in an unambiguous form) and depending on the same number of parameters, i.e., force constants, when independent coordinates (natural or symmetry) are used in its description.

In contrast with carbon nanotubes, the absence of translational symmetry (or periodical boundary condition) in the restricted direction of zigzag graphene nanoribbon removes the selection rule of subband number conservation. However, zigzag graphene nanoribbons with even dimers do have the inversion symmetry. We, therefore, propose a selection rule of parity conservation for electron-phonon interactions. The electron-phonon scattering matrix in zigzag graphene nanoribbons is developed using the tight-binging model within the deformation potential approximation.

The chemical functionalization of endohedral (metallo)fullerenes has become a main focus of research in the last few years. It has been found that the reactivity of endohedral (metallo)fullerenes may be quite different from that of the empty fullerenes. Encapsulated species have an enormous influence on the thermodynamics, kinetics, and regiochemistry of the exohedral addition reactions undergone by these species. A detailed understanding of the changes in chemical reactivity due to incarceration of atoms or clusters of atoms is essential to assist the synthesis of new functionalized endohedral fullerenes with specific properties. Herein, we report the study of the Diels-Alder cycloaddition between 1,3-butadiene and all nonequivalent bonds of the Ti(2)C(2)@D(3h)-C(78) metallic carbide endohedral metallofullerene (EMF) at the BP86/TZP//BP86/DZP level of theory. The results obtained are compared with those found by some of us at the same level of theory for the D(3h)-C(78) free cage and the M(3)N@D(3h)-C(78) (M=Sc and Y) metallic nitride EMFs. It is found that the free cage is more reactive than the Ti(2)C(2)@D(3h)-C(78) EMF and this, in turn, has a higher reactivity than M(3)N@D(3h)-C(78). The results indicate that, for Ti(2)C(2)@D(3h)-C(78), the corannulene-type [5,6] bonds c and f, and the type B [6,6] bond 3 are those thermodynamically and kinetically preferred. In contrast, the D(3h)-C(78) free cage has a preference for addition to the [6,6] 1 and 6 bonds and the [5,6] b bond, whereas M(3)N@D(3h)-C(78) favors additions to the [6,6] 6 (M=Sc) and [5,6] d (M=Y) bonds. The reasons for the regioselectivity found in Ti(2)C(2)@D(3h)-C(78) are discussed.

Full Text Available We present new dispersion and hydrogen bond corrections to the PM6 method, PM6-D3H+, and its implementation in the GAMESS program. The method combines the DFT-D3 dispersion correction by Grimme et al. with a modified version of the H+ hydrogen bond correction by Korth. Overall, the interaction energy of PM6-D3H+ is very similar to PM6-DH2 and PM6-DH+, with RMSD and MAD values within 0.02 kcal/mol of one another. The main difference is that the geometry optimizations of 88 complexes result in 82, 6, 0, and 0 geometries with 0, 1, 2, and 3 or more imaginary frequencies using PM6-D3H+ implemented in GAMESS, while the corresponding numbers for PM6-DH+ implemented in MOPAC are 54, 17, 15, and 2. The PM6-D3H+ method as implemented in GAMESS offers an attractive alternative to PM6-DH+ in MOPAC in cases where the LBFGS optimizer must be used and a vibrational analysis is needed, e.g., when computing vibrational free energies. While the GAMESS implementation is up to 10 times slower for geometry optimizations of proteins in bulk solvent, compared to MOPAC, it is sufficiently fast to make geometry optimizations of small proteins practically feasible.

Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy of the elastic constants and the interplay of the relevant lengths scales, such as the correlation length and the surface geometrical parameters. Transitions between different textures, usually with different symmetries, may occur under a wide range of conditions. We use the Landau-de Gennes free energy to investigate the texture of nematics in sinusoidal channels with parallel anchoring bounded by nematic-air interfaces that favour perpendicular (hometropic) anchoring. In micron size channels 5CB was observed to exhibit a non-trivial texture characterized by a disclination line, within the channel, which is broken into a zigzag pattern. Our calculations reveal that when the elastic anisotropy of the nematic does not favour twist distortions the defect is a straight disclination line that runs along the channel, which breaks into a zigzag pattern with a characteristic period, when the twist elastic constant becomes sufficiently small when compared to the splay and bend constants. The transition occurs through a twist instability that drives the defect line to rotate from its original position. The interplay between the energetically favourable twist distortions that induce the defect rotation and the liquid crystal anchoring at the surfaces leads to the zigzag pattern. We investigate in detail the dependence of the periodicity of the zigzag pattern on the geometrical parameters of the sinusoidal channels, which in line with the experimental results is found to be non-linear.

The tight-binding model including the spin-orbit coupling (SOC) is used to study electronic and optical properties of zigzag silicene nanoribbons (ZSiNRs) in magnetic and electric fields. The SOC affects the low-energy bands and induces new selection rules leading to richer optical spectra. Except an increase in bandgaps, perpendicular magnetic field further exhibits spin-polarized Landau levels, in which electron's probability density of band-edge states distributes like a standing-wave. Landau levels could enhance the DOS and increases absorption frequency and strength. Perpendicular electric field (Fz) increases bandgap and thus absorption frequency, but it does not change band symmetry, edge-states, and selection rules. Moreover, Fz enhances the split of spin-polarized states inducing more absorption peaks. Parallel electric field (Fx) leads to an overlap between conduction and valence bands and destroys band symmetry and Landau levels. Consequently, Fx exhibits new selection rules and enriches absorption spectra.

The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...

Edge states and magnetism are crucial for spintronic applications of nanoribbons. Here, using first-principles calculations, we explore structural stabilities and electronic properties of zigzag silicene nanoribbons (ZSiNRs) with Klein and pentagon-heptagon reconstructions. Comparing to unreconstructed zigzag edges, deformed bare pentagon-heptagon ones are favored under H-poor conditions, while H-rich surroundings stabilize di-hydrogenated Klein edges. These Klein edges have analogous magnetism to zigzag ones, which also possess the electric-field-induced half-metallicity of nanoribbons. Moreover, diverse magnetic states can be achieved by asymmetric Klein and zigzag edges into ZSiNRs, which could be transformed from antiferromagnetic-semiconductors to bipolar spin-gapless-semiconductors and ferromagnetic-metals depending on edge hydrogenations.

The Zitterbewegung of a wave packet in a zigzag graphene nanoribbon is theoretically investigated. The coupling between edge states and bulk states results in intriguing properties. Apart from the oscillation in position perpendicular to the direction of motion, we also observe an oscillation along the direction of propagation which is not present in semiconductor nanowires or infinite graphene sheets. We also observe a resonance of its amplitude with respect to the central momentum of the wave packet. We show here that this longitudinal Zitterbewegung is caused by the interplay between bulk and edge states, which is a unique property of a zigzag nanoribbon.

Monolayered titanium disulfide TiS2, a prospective nanoelectronic material, was previously shown to be subject to an exothermic solid-state D3h -D3d reaction that proceeds via a newly discovered transition state. Here, we study the reaction in detail using topological methods of quantum chemistry (quantum theory of atoms in molecules and electron localization function analysis) and show how electron density and chemical bonding between the atoms change in the course of the reaction. The reaction is shown to undergo a series of topological catastrophes, associated with elementary chemical events such as break and formation of bonds (including the unexpected formation of S-S bonding between sulfur layers), and rearrangement of electron density of outer valence and core shells.

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.

The novel hydrocarbon propeller-shaped D3h-symmetric cyclophane (3), "anthraphane", was prepared through a revisited and optimized gram-scale synthesis of the key building block anthracene-1,8-ditriflate 7. Anthraphane has a high tendency to crystallize and single crystals in size ranges of 100-200 μm are easily obtained from different solvents. The crystallization behavior of 3 was extensively studied to unravel packing motifs and determine whether the packing can be steered into a desired direction, so to allow topochemical photopolymerization. SC-XRD shows that anthraphane packs in layers irrespective of the solvent used for crystallization. However, within the layers, intermolecular arrangements and π-π interactions of the anthracene units vary strongly. Four interaction motifs for the anthracene moieties are observed and discussed in detail: two types of exclusively edge-to-face (etf), a mixture of edge-to-face and face-to-face (ftf), and no anthracene-anthracene interaction at all. To elucidate why an exclusive ftf stacking was not observed, electrostatic potential surface (EPS) calculations with the semiempirical PM3 method were performed. They show qualitatively that the anthracene faces bear a strong negative surface potential, which may be the cause for this cyclophane to avoid ftf interactions. This combined crystallographic and computational study provides valuable insights on how to create all-ftf packings.

The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of single cell amoeba: in the absence of an external cue, free amoebae move randomly with a noisy, yet, discernible sequence of 'run-and-turns' analogous to the 'run-and-tumbles' of swimming bacteria. Interestingly, amoeboid trajectories favor zigzag turns. In other words, the cells bias their crawling by making a turn in the opposite direction to a previous turn. This property enhances the long range directional persistence of the moving trajectories. This study proposes that such a zigzag crawling behavior can be a general property of any crawling cells by demonstrating that 1) microglia, which are the immune cells of the brain, and 2) a simple rule-based model cell, which incorporates the actual biochemistry and mechanics behind cell crawling, both exhibit similar type of crawling behavior. Almost all legged animals walk by alternating their feet. Similarly, all crawling cells appear to move forward by alternating the direction of their movement, even though the regularity and degree of zigzag preference vary from one type to the other.

Superconductivity has recently been discovered in Pr{sub 2}Ba{sub 4}Cu{sub 7}O{sub 15-{delta}} with a maximum T{sub c} of about 15K. Since the CuO planes in this material are believed to be insulating, it has been proposed that the superconductivity occurs in the double (or zigzag) CuO chain layer. On phenomenological grounds we propose a theoretical interpretation of the experimental results in terms of a new phase for the zigzag chain, labelled by C{sub 1}S{sub 3/2}. This phase has a gap in the relative charge mode and a partial gap in the relative spin mode. It has gapless uniform charge and spin excitations and can have a divergent superconducting susceptibility, even for repulsive interactions. A microscopic model for the zigzag CuO chain is proposed, and on the basis of density matrix renormalization group (DMRG) and bosonization studies, we adduce evidence that supports our proposal.

Full Text Available The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of single cell amoeba: in the absence of an external cue, free amoebae move randomly with a noisy, yet, discernible sequence of 'run-and-turns' analogous to the 'run-and-tumbles' of swimming bacteria. Interestingly, amoeboid trajectories favor zigzag turns. In other words, the cells bias their crawling by making a turn in the opposite direction to a previous turn. This property enhances the long range directional persistence of the moving trajectories. This study proposes that such a zigzag crawling behavior can be a general property of any crawling cells by demonstrating that 1 microglia, which are the immune cells of the brain, and 2 a simple rule-based model cell, which incorporates the actual biochemistry and mechanics behind cell crawling, both exhibit similar type of crawling behavior. Almost all legged animals walk by alternating their feet. Similarly, all crawling cells appear to move forward by alternating the direction of their movement, even though the regularity and degree of zigzag preference vary from one type to the other.

The consequences of some symmetries of the three-alpha system are discussed. In particular, the recent description of the low-energy spectrum of the 12C nucleus in terms of the Algebraic Cluster Model (ACM) is compared to that of the Semimicroscopic Algebraic Cluster Model (SACM). The previous one applies interactions of a D3h geometric symmetry [1], while the latter one has a U(3) multichannel dynamical symmetry, that connects the shell and cluster pictures. The available data is in line with both descriptions.

Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry-dependent...

Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model-due, in particular, to the geometry......-dependent anharmonism that comes into the picture. The existence or otherwise of solitons is determined in this case by the interplay between the geometrical anharmonism and the physical anharmonism of the interstitial interaction, of opposite signs. The nonlinear dynamic analysis of the three most typical zigzag...... models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton...

Using non-equilibrium green function with density functional theory, the present study investigates the transport properties of decorated zigzag graphene nanoribbon with a copper cluster. We have represented the decoration of zigzag graphene nanoribbon with single copper atom and cluster containing two and three copper atoms. In all the cases, copper atoms tend to occupy the edge state. In addition, we have shown that copper can alter the current-voltage characteristic of zigzag graphene nanoribbon and create new fluctuations and negative differential resistance. These alternations are made due to discontinuity in the combination of orbitals along the graphene nanoribbon. Decoration alters these discontinuities and creates more visible fluctuations. However, in low bias voltages, the changes are similar in all the cases. The study demonstrates that in the decorated zigzag graphene nanoribbon, the edge states are the main states for transporting electron from one electrode to another.

A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within specified boundaries from the material. Based on a graph-theoretical formulation, the algorithmic handling of one particular machining problem {open_quote}zigzag pocket machining{close_quote} is investigated. We present a linear-time algorithm that ensures that no region of the pocket is machined repeatedly, thereby attempting to minimize the number of tool retractions required. This problem is shown to be NP-hard for pockets with holes. Our algorithm is a provable good in the sense that the machining path generated for a pocket with h holes requires at most 5. OPT+ 6 - h retractions, where OPT is the (unknown) minimum number of retractions required by any algorithm. The algorithm has been implemented, and practical tests for pockets without holes clearly showed that one can expect an approximation factor of about 1.5 for practical examples, rather than the factor 5 as proved by our analysis.

The electronic properties of zigzag graphene oxide nanoribbons (ZGOR) are presented. The results show interesting behaviors which are considerably different from the properties of the perfect graphene nanoribbons (GNRs). The theoretical methods include a Huckel-tight binding approach, a Green's function methodology, and the Landauer formalism. The presence of oxygen on the edge results in band bending, a noticeable change in density of states and thus the conductance. Consequently, the occupation in the valence bands increase for the next neighboring carbon atom in the unit cell. Conductance drops in both the conduction and valence band regions are due to the reduction of allowed k modes resulting from band bending. The asymmetry of the energy band structure of the ZGOR is due to the energy differences of the atoms. The inclusion of a foreign atom's orbital energies changes the dispersion relation of the eigenvalues in energy space. These novel characteristics are important and valuable in the study of quantum transport of GNRs.

We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.

In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. The full non-rigid group (f-NRG) of dimethyltrichlorophosphorus with the symmetry group D3h was studied. It has been proven that it is a group of order 216 with 27 conjugacy classes and its character table computed. Finally, the Permutation-lnversion group of this molecule was calculated.

The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

Full Text Available The charge transport properties of zigzag graphene nanoribbons (ZGNRs under uniaxial and shear strains are theoretically studied. Although all strained ZGNRs have similar metallic band structures, they show four types of transport behavior under bias voltages that depend on the type of strain and the mirror symmetry of the ZGNR. Under an applied uniaxial strain, the current of symmetric ZGNRs is consistently small, while for asymmetric ZGNRs it is large. In contrast, the current increases with increasing shear strain for symmetric ZGNRs while it decreases for asymmetric ZGNRs. The current properties merge when the shear strain exceeds a critical value, and the two systems then show similar behavior. Our results suggest that strained ZGNRs with an appropriate applied shear are ideal conducting wires.

We derive an analytic description of the spin susceptibility in finite length zigzag carbon nanotubes (CNT) with chirality (n, 0). The spin susceptibility is proportional to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions which describes indirect carrier mediated exchange coupling between localized magnetic moments. We show that the strongest RKKY interactions are along the edges of the nanotube and in the thermodynamic limit at half filling with spin symmetry the shape of the susceptibility curve about the edge of the CNT can be determined solely by the lattice geometry represented by the parameter n and a parameter L which describes the nanotube length. We also show that the introduction of Zeeman splitting or doping may have no effect on the spin susceptibility, provided n is small. A detailed knowledge of magnetic interactions, such as RKKY interactions, in CNT is of vital importance to the development of nanotechnology applications.

In planar ${\\cal N}=4$ supersymmetric Yang-Mills theory we have studied supersymmetric Wilson loops composed of a large number of light-like segments, i.e., null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

In planar {N}=4 supersymmetric Yang-Mills theory we have studied one kind of (locally) BPS Wilson loops composed of a large number of light-like segments, i.e. null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory, we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

Ion transport through nanoporous systems has attracted broad interest due to its crucial role in physiological processes in living organisms and artificial bionic devices. In this work, a nanochannel system with a zigzag inner surface was fabricated by using a two-step anodizing technique. The rectification performance of the zigzag channels was observed by I-V measurement in KCl solution. Unlike channels with asymmetric geometry, the mechanism was analyzed based on the "point effect" of charge distribution and "shape effect" of the zigzag channel. The current rectification ratio decreases from nearly 3.0 to 1.0 when the KCl concentration increased from 0.1 mM to 100 mM. The fabrication of different nanopore systems and exploration of novel mechanisms will help to develop biomimetic membranes for practical applications.

Full Text Available Pocket-milling operations are widely used for scooping out materials during the machiningof aircraft components. This paper presents a tool-path planning algorithm for pocket-millingusing zig-zag method. The algorithm consists of basically three modules, viz., generating toolpathelements using pocket geometry entities as input, finding out intersection points (edgepoints, and rearranging points in a zig-zag fashion. OPTPATH algorithm1,2 is used for generatingtool-path elements. These elements thus generated are used to find out the intersection pointswith all entities. The valid points are arranged in a zig-zag way, which are used for machiningany pocket considered. This algorithm works satisfactorily for all the pocket boundaries havingline-line, line-arc, and arc-arc geometry entities.

The zigzag edge of a graphene nanoribbon possesses a unique electronic state that is near the Fermi level and localized at the edge carbon atoms. We investigate the chemical reactivity of these zigzag edge sites by examining their reaction energetics with common radicals from first principles. A "partial radical" concept for the edge carbon atoms is introduced to characterize their chemical reactivity, and the validity of this concept is verified by comparing the dissociation energies of edge-radical bonds with similar bonds in molecules. In addition, the uniqueness of the zigzag-edged graphene nanoribbon is further demonstrated by comparing it with other forms of sp2 carbons, including a graphene sheet, nanotubes, and an armchair-edged graphene nanoribbon.

A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. Exact solutions for simply supported and cantilevered beams subjected to static loads are derived and the improved modelling capability of the new zigzag beam theory is demonstrated. In particular, extensive results for thick beams with highly heterogeneous material lay-ups are discussed and compared with corresponding results obtained from elasticity solutions, two other zigzag theories, and high-fidelity finite element analyses. Comparisons with the baseline Timoshenko Beam Theory are also presented. The comparisons clearly show the improved accuracy of the new, refined zigzag theory presented herein over similar existing theories. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining relatively low-cost, accurate estimates of structural response needed to design an important class of high-performance aerospace structures.

Full Text Available A comprehensive theoretical study of the half-metallicity in the zigzag graphene nanoribbons (ZGNRs by adsorption of the zigzag hydrogen fluoride chains was presented. The ZGNR by adsorption of the hydrogen fluoride chains could be half-metallic when a critical length of the hydrogen fluoride chain is achieved on the ZGNR at low temperature. It was found that the strong dipole moments of the hydrogen fluoride chains act as the constant electric field. Our results suggest a huge possibility in spintronics device applications for achieving half-metallicity in the ZGNRs without the excessively high external electric fields.

This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...

The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same representation category. In this paper we try to establish that every quantum field theory satisfying some basic axioms posseses a weak quasi Hopf algebra as gauge symmetry. The first step is to construct a functor from the representation category to the category of finite dimensional vector spaces. Given such a functor we can use a generalized reconstruction theorem to find the symmetry algebra. It is shown how this symmetry algebra is used to build a gauge covariant field algebra and we investigate the question why this generality is necessary.

We study a generalization of the Frenkel-Kontorova model which describes a zig-zag chain of particles coupled by both the first- and second-neighbor harmonic forces and subjected to a planar substrate with a commensurate potential relief. The particles are supposed to have two degrees of freedom:...

We report a systematic theoretical investigation of the effects of metal substrates on the local magnetic moments of zigzag graphene nanoribbons (ZGNRs). Representative metal surfaces of Au, Pt, Ni, Cu, Al, Ag, and Pd have been analyzed from atomic first principles. Results show that the local ma...

We examine the temperature dependence of graphene edge terminations at the atomic scale using an in situ heating holder within an aberration-corrected transmission electron microscope. The relative ratios of armchair, zigzag, and reconstructed zigzag edges from over 350 frames at each temperature are measured. Below 400 °C, the edges are dominated by zigzag terminations, but above 600 °C, this changes dramatically, with edges dominated by armchair and reconstructed zigzag edges. We show that at low temperature chemical etching effects dominate and cause deviation to the thermodynamics of the system. At high temperatures (600 and 800 °C), adsorbates are evaporated from the surface of graphene and chemical etching effects are significantly reduced, enabling the thermodynamic distribution of edge types to be observed. The growth rate of holes at high temperature is also shown to be slower than at room temperature, indicative of the reduced chemical etching process. These results provide important insights into the role of chemical etching effects in the hole formation, edge sputtering, and edge reconstruction in graphene.

The calculation of the complex matrixes in odd triangular symmetry was accomplished.The configurations of the coordination unit with various triangular symmetries and different ligand numbers were discussed.On the basis of the double-sphere coordination point-charge (DSCPCF) model,the detailed forms of the DSCPCF parameters Bmk and the expressions of the perturbation matrix elements in triangular field (D3,D3h,D3d) were derived.Thereby,the calculation scheme of coordination field perturbation energy of the rare earth complexes with triangular symmetry was constructed After the calculation scheme was programmed,the Stark energies of the crystalline TbAl3(BO3)4 were calculated The results were considerably close to the experimental values

In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

The spin-polarized transport properties of helical zigzag graphene nanoribbons (ZGNRs) are investigated by first-principles calculations. It is found that although all helical ZGNRs have similar density of states and edge states, they show obviously different transport characteristics depending on the curling manners. ZGNRs curled along zigzag orientation exhibit perfect spin filtering effect with a large spin-split gap near the Fermi level, while ZGNRs curled along armchair orientation behave as conventional conductors for both two spin channels. The spin filtering effect will be weakened with the increase of either ribbon width or curling diameter. The results suggest that ultrasmall helical ZGNRs have important potential applications in spintronics and flexible electronics. - Highlights: • Perfect spin filtering effect has been found in helical ZGNRs. • The effect strongly depends on the curling manners of ZGNRs. • Different transport properties do not induced by distinct electronic properties. • The effect may be weakened with increasing either ribbon width or curling diameter.

We perform a density functional study on the adsorption and diffusion of Li atoms on silicene sheet and zigzag nanoribbons. Our results show that the diffusion energy barrier of Li adatoms on silicene sheet is 0.25 eV, which is much lower than on graphene and Si bulk. The diffusion barriers along the axis of zigzag silicene nanoribbon range from 0.1 to 0.25 eV due to an edge effect, while the diffusion energy barrier is about 0.5 eV for a Li adatom to enter into a silicene nanoribbon. Our calculations indicate that using silicene nanoribbons as anodes is favorable for a Li-ion battery. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074212 and 11204123) and the Natural Science Foundation of Jiangsu province, China (Grant No. BK20130945).

Electronic properties of multi-defected zigzag single-walled carbon nanotubes are investigated by use of the tight-binding Green’s function method. The Stone-Wales defects and the vacancies are considered. We find that the conductance sensitively depends on the realistic defect configurations for the metallic zigzag carbon nanotubes. Interestingly, the electronic transport properties of the nanotubes with three vacancies can be considered as the sum effect of two double-vacancies, while those with Stone-Wales defects can not. The electron interference along the longitudinal axis and the transport blocking are observed, which may be useful for understanding the electron transport behavior of carbon nanotube in experiments.

Full Text Available We propose a graphene nanoribbon-based heterojunction, where a defect-free interface separates two zigzag graphene nanoribbons prepared in opposite antiferromagnetic spin configurations. This heterospin junction is found to allow the redirecting of low-energy electrons from one edge to the other. The basic scattering mechanisms and their relation to the system’s geometry are investigated through a combination of Landauer–Green’s function and the S-matrix and eigen-channel methods within a tight-binding + Hubbard model validated with density functional theory. The findings demonstrate the possibility of using zigzag-edged graphene nanoribbons (zGNRs in complex networks where current can be transmitted across the entire system, instead of following the shortest paths along connected edges belonging to the same sub-lattice.

The spin-polarized transport properties of helical zigzag graphene nanoribbons (ZGNRs) are investigated by first-principles calculations. It is found that although all helical ZGNRs have similar density of states and edge states, they show obviously different transport characteristics depending on the curling manners. ZGNRs curled along zigzag orientation exhibit perfect spin filtering effect with a large spin-split gap near the Fermi level, while ZGNRs curled along armchair orientation behave as conventional conductors for both two spin channels. The spin filtering effect will be weakened with the increase of either ribbon width or curling diameter. The results suggest that ultrasmall helical ZGNRs have important potential applications in spintronics and flexible electronics.

We report the thermally induced unconventional cracking of graphene to generate zigzag edges. This crystallography-selective cracking was observed for as-grown graphene films immediately following the cooling process subsequent to chemical vapor deposition (CVD) on Cu foil. Results from Raman spectroscopy show that the crack-derived edges have smoother zigzag edges than the chemically formed grain edges of CVD graphene. Using these cracks as nanogaps, we were also able to demonstrate the carrier tuning of graphene through the electric field effect. Statistical analysis of visual observations indicated that the crack formation results from uniaxial tension imparted by the Cu substrates together with the stress concentration at notches in the polycrystalline graphene films. On the basis of simulation results using a simplified thermal shrinkage model, we propose that the cooling-induced tension is derived from the transient lattice expansion of narrow Cu grains imparted by the thermal shrinkage of adjacent Cu grains.

Zigzag edges of graphene nanostructures host localized electronic states that are predicted to be spin-polarized. However, these edge states are highly susceptible to edge roughness and interaction with a supporting substrate, complicating the study of their intrinsic electronic and magnetic structure. Here, we focus on atomically precise graphene nanoribbons whose two short zigzag edges host exactly one localized electron each. Using the tip of a scanning tunnelling microscope, the graphene nanoribbons are transferred from the metallic growth substrate onto insulating islands of NaCl in order to decouple their electronic structure from the metal. The absence of charge transfer and hybridization with the substrate is confirmed by scanning tunnelling spectroscopy, which reveals a pair of occupied/unoccupied edge states. Their large energy splitting of 1.9 eV is in accordance with ab initio many-body perturbation theory calculations and reflects the dominant role of electron-electron interactions in these localized states.

Similar to rolling up paper, carbon nanoscrolls (CNSs) can be rolled from graphene nanoribbons (GNRs) using physical approaches. Owing to their peculiar one-dimensional nanostructures, CNSs have attracted great attention over the past few years. In this study, we have investigated the effects of bending deformation on the electronic properties of zigzag CNSs (ZCNSs) during the rolling process from zigzag GNRs (ZGNRs) by means of first-principles calculations. It is found that a metal-semiconductor-metal transition is observed. By analyzing charge density and density of states, the origin of this electronic property transition is discussed. Furthermore, we find that the metal-semiconductor-metal transition in ZCNSs is independent of ribbon width as well as spin-orbit interaction. Our results of the metal-semiconductor-metal transition in the ZCNSs are robust and may open potential applications in nano-electromechanical devices based on the ZCNSs.Similar to rolling up paper, carbon nanoscrolls (CNSs) can be rolled from graphene nanoribbons (GNRs) using physical approaches. Owing to their peculiar one-dimensional nanostructures, CNSs have attracted great attention over the past few years. In this study, we have investigated the effects of bending deformation on the electronic properties of zigzag CNSs (ZCNSs) during the rolling process from zigzag GNRs (ZGNRs) by means of first-principles calculations. It is found that a metal-semiconductor-metal transition is observed. By analyzing charge density and density of states, the origin of this electronic property transition is discussed. Furthermore, we find that the metal-semiconductor-metal transition in ZCNSs is independent of ribbon width as well as spin-orbit interaction. Our results of the metal-semiconductor-metal transition in the ZCNSs are robust and may open potential applications in nano-electromechanical devices based on the ZCNSs. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr07628

Full Text Available The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.

A set of conformations obtained from explicit solvent molecular dynamics (MD) simulations of the Sarcin-Ricin internal loop (SRL) RNA motif is investigated using quantum mechanical (QM, TPSS-D3/def2-TZVP DFT-D3) and molecular mechanics (MM, AMBER parm99bsc0+χol3 force field) methods. Solvent effects are approximated using implicit solvent methods (COSMO for DFT-D3; GB and PB for MM). Large-scale DFT-D3 optimizations of the full 11-nucleotide motif are compared to MM results and reveal a higher flexibility of DFT-D3 over the MM in the optimization procedure. Conformational energies of the SRL motif expose significant differences in the DFT-D3 and MM energy descriptions that explain difficulties in MD simulations of the SRL motif. The TPSS-D3 data are in excellent agreement with results obtained by the hybrid functionals PW6B95-D3 and M06-2X. Computationally more efficient methods such as PM6-D3H and HF-3c show promising but partly inconsistent results. It is demonstrated that large-scale DFT-D3 computations on complete nucleic acids building blocks are a viable tool to complement the picture obtained from MD simulations and can be used as benchmarks for faster computational methods. Methodological challenges of large-scale QM computations on nucleic acids such as missing solvent-solute interactions and the truncation of the studied systems are discussed.

In this paper, we consider zigzag-edge germanene nanoribbons with small buckling and even (symmetric) or odd (asymmetric) widths. Although the band structures of these two type structures are the same, they are noticeably different in terms of conductivity and current. In previous works on silicene, the role of buckling to dominate the effect of symmetry has been ignored and just the buckling changes of the symmetry space group from σ to C 2 are shown. In this case, buckling is the main factor responsible for differences in conductivity and current. Fluorine, hydroxyl, and hydrogen are used to passivate the nanoribbon edges. Results show that the current and conductivity are strongly dependent on the kinds of substitutional atoms/groups used to passivate the structure. It is found that symmetry breaking is not the only effective factor in the creation of current—buckling and backscattering are also important.

Full Text Available A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice is more expressive than πsep (its subset with only separate choice. The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel when running two copies in parallel. In both proofs, the role of breaking (initial symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential.

The class of RMn{sub 2}O{sub 5} (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn{sup 4+} and Mn{sup 3+} magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

The magnetization plateaux in two dimensionally coupled S=1/2 dimerized zigzag Heisenberg chains are investigated by means of the bond operator mean field approximation. In the absence of the interchain coupling, this model is known to have a plateau at half of the saturation magnetization accompanied by the spontaneous translational symmetry breakdown. The parameter regime in which the plateau appears is reproduced well within the present approximation. In the presence of the interchain coupling, this plateau is shown to be suppressed. This result is also supported by the numerical diagonalization calculation.

@@ Based on the density functional theory, we calculate the dependence of the band structures of bilaver ziezaff-edzed grapnene nanonooons(BZGNRs) upon ribbon width, interlayer distance and stacking styles.Unlike monolayer zigzag GNR, whose energy gap is always zero under different ribbon widths, the gap of BZGNR varies greathy with the ribbon width or the interlayer distance.The greatest gaps for AA-stacking and AB-stacking BZGNRs are about 0.22eV and 0.12eV, respectively, which implies that gap-tuning of AA-BZGNRs is more effective than that of AB-BZGNRs.These results present a way to tune the band structures of BZGNRs and also provide theoretical guidance for the fabrication of GNR-based piezoelectric devices.%Based on the density functional theory, we calculate the dependence of the band structures of bilayer zigzag-edged graphene nanoribbons (BZGNRs) upon ribbon width, interlayer distance and stacking styles. Unlike monolayer zigzag GNR, whose energy gap is always zero under different ribbon widths, the gap of BZGNR varies greatly with the ribbon width or the interlayer distance. The greatest gaps for AA-stacking and AR-stacking BZGNRs are about 0.22 eV and O.12eV, respectively, which implies that gap-tuning of AA-BZGNRs is more effective than that of AB-BZGNRs. These results present a way to tune the band structures of BZGNRs and also provide theoretical guidance for the fabrication of GNR-based piezoelectric devices.

A well-known result by Palamidessi tells us that {\\pi}mix (the {\\pi}-calculus with mixed choice) is more expressive than {\\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\\pi}mix i...

A well-known result by Palamidessi tells us that \\pimix (the \\pi-calculus with mixed choice) is more expressive than \\pisep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from \\pimix into \\pisep. We...

Magnetoband structures of AB-stacked zigzag nanographite ribbons are studied by the tight-binding model. The magnetic field changes band width, energy space, and energy dispersions (the produce of Landau subbands and Landau levels). It causes many zero energy points. Such points and corresponding localized states are studied in detail. There are certain important differences between localized states and edge states. Oscillation period of Landau subbands are determined by these points. The interribbon interactions also affect magnetoband structures, such as energy dispersions, band width, oscillation period of Landau subbands, and flux dependence of Hofstadter butterflies.

We explore the nonequilibrium dynamics of two coupled zig-zag chains of trapped ions in a double well potential. Following a quench of the potential barrier between both wells, the induced coupling between both chains due to the long-range interaction of the ions leads to their complete melting. The resulting dynamics is however not exlusively irregular but leads to phases of motion during which quasistationary structures appear with the ions arranged in a plethora of ordered and symmetric configurations. A normal mode analysis shows that distinguished modes lead to the decisive population transfer responsible for this sequence of regular and irregular structures.

Zigzag graphene nanoribbons (ZGNRs) are known to exhibit metallic behavior. Depending on structural properties such as edge status, doping and width of nanoribbons, the electronic properties of these structures may vary. In this study, changes in electronic properties of crystal by doping Lithium (Li) atom to ZGNR structure are analyzed. In spin polarized calculations are made using Density Functional Theory (DFT) with generalized gradient approximation (GGA) as exchange correlation. As a result of calculations, it has been determined that Li atom affects electronic properties of ZGNR structure significantly. It is observed that ZGNR structure exhibiting metallic behavior in pure state shows half-metal and semiconductor behavior with Li atom.

We study theoretically the electronic transport properties of zigzag silicene nanoribbon superlattices subject to a periodic electric field perpendicular to the surface of silicene. Our results show that the conductivity of the system depends on the superlattice structural parameters and show effects analogous to those found with two-dimensional semiconductor superlattices. For a superlattice with Nb barriers, a series of resonant peaks, each of which is split into (Nb - 1) subpeaks, and transmission blockade regions appear in the conductance spectrum, which indicates the formation of minibands and minigaps. These silicene-based quantum structures can provide concepts for the design nanodevices.

Full Text Available We fabricated graphene nanoribbons (GNRs chemically derived from expandable graphite. All GNRs exhibit atomically smooth edges that extended over their entire length. We investigated four of the fabricated GNRs using Raman spectroscopy. Two of the investigated GNRs show Raman spectra with a missing D-band peak, while D-band peaks can be clearly observed for the other two GNRs. The two GNRs which do not show the D-band peak are GNRs with zigzag edges, and the two other GNRs which show clearly the D-band peaks are possibly GNRs with armchair edges.

Curie temperature T{sub C} has important implications for the experimental realization of magnetic graphone nanostructures relevant for future spintronic applications. Using both Monte Carlo method and mean field theory, we study magnetic properties of zigzag graphone nanoribons (ZGONR) doped with magnetic impurities M. We show that T{sub C} increases with the number of dopants but for configurations with fixed number M, T{sub C} is not very sensitive to impurities distances d(M−M). In particular, in bidoped ZGONR configurations, T{sub C} has different values for the same d(M−M). This surprising behavior stems from edge effect. The result as derived in this report is easily adapted to predict how the magnetism is influenced in all half hydrogenated four-electrons hexagonal nanoribbon devices. - Highlights: • We investigate the possibility of controlling the magnetism in zigzag graphone nanoribbons. • We study different configurations of Mono-, bi- and tri-doped ZGONR by TM impurities. • We show that Curie temperature is more sensitive to edges than impurities distances. • We provide a qualitative way of determining which maximal and minimal TC for wide ZGONRs.

Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model ...

Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)

Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads to one of the most successful theories in modern particle physics. In this short talk, I shall try to give a taste of this beautiful and exciting concept.

Complexin prevents SNAREs from releasing neurotransmitters until an action potential arrives at the synapse. To understand the mechanism for this inhibition, we determined the structure of complexin bound to a mimetic of a prefusion SNAREpin lacking the portion of the v-SNARE that zippers last to trigger fusion. The 'central helix' of complexin is anchored to one SNARE complex, while its 'accessory helix' extends away at {approx}45{sup o} and bridges to a second complex, occupying the vacant v-SNARE binding site to inhibit fusion. We expected the accessory helix to compete with the v-SNARE for t-SNARE binding but found instead that the interaction occurs intermolecularly. Thus, complexin organizes the SNAREs into a zigzag topology that, when interposed between the vesicle and plasma membranes, is incompatible with fusion.

Complexin prevents SNAREs from releasing neurotransmitters until an action potential arrives at the synapse. To understand the mechanism for this inhibition, we determined the structure of complexin bound to a mimetic of a prefusion SNAREpin lacking the portion of the v-SNARE that zippers last to trigger fusion. The 'central helix' of complexin is anchored to one SNARE complex, while its 'accessory helix' extends away at {approx}45 deg. and bridges to a second complex, occupying the vacant v-SNARE binding site to inhibit fusion. We expected the accessory helix to compete with the v-SNARE for t-SNARE binding but found instead that the interaction occurs intermolecularly. Thus, complexin organizes the SNAREs into a zigzag topology that, when interposed between the vesicle and plasma membranes, is incompatible with fusion.

The magnetism of graphene has remained divergent and controversial due to absence of reliable experimental results. Here we show the intrinsic magnetism of graphene edge states revealed based on unidirectional aligned graphene sheets derived from completely carbonized SiC crystals. It is found that ferromagnetism, antiferromagnetism and diamagnetism along with a probable superconductivity exist in the graphene with irregular zigzag edges. A phase diagram is constructed to show the evolution of the magnetism. The ferromagnetic ordering curie-temperature of the fundamental magnetic order unit (FMOU) is 820 ± 80 K. The antiferromagnetic ordering Neel temperature of the FMOUs belonging to different sublattices is about 54 ± 2 K. The diamagnetism is similar to that of graphite and can be well described by the Kotosonov's equation. Our experimental results provide new evidences to clarify the controversial experimental phenomena observed in graphene and contribute to a deeper insight into the nature of magnetism in graphene based system.

We explore the non-equilibrium dynamics of two coupled zig-zag chains of trapped ions in a double well potential. Following a quench of the potential barrier between both wells, the induced coupling between both chains due to the long-range interaction of the ions leads to the complete loss of order in the radial direction. The resulting dynamics is however not exclusively irregular but leads to phases of motion during which various ordered structures appear with ions arranged in arcs, lines and crosses. We quantify the emerging order by introducing a suitable measure and complement our analysis of the ion dynamics using a normal mode analysis showing a decisive population transfer between only a few distinguished modes.

The adiabatic electron transport is theoretically studied in a zigzag graphene nanoribbon (ZGNR) junction with two time-dependent pumping electric fields. By modeling a ZGNR p–n junction and applying the Keldysh Green’s function method, we find that a pumped charge current is flowing in the device at a zero external bias, which mainly comes from the photon-assisted tunneling process and the valley selection rule in an even-chain ZGNR junction. The pumped charge current and its ON and OFF states can be efficiently modulated by changing the system parameters such as the pumping frequency, the pumping phase difference, and the Fermi level. A ferromagnetic ZGNR device is also studied to generate a pure spin current and a fully polarized spin current due to the combined spin pump effect and the valley valve effect. Our finding might pave the way to manipulate the degree of freedom of electrons in a graphene-based electronic device.

We demonstrate the large bending deformation induced by an array of permanent magnets (applied field ∼0.02 T) designed to minimize poles in the bent state of the crystal. Planar cantilevers of NiMnGa (5M modulated martensite) ferromagnetic shape memory alloy deform into an arched shape according to theory, with a zig-zag microstructure that complies with the kinematic and magnetic compatibility between adjacent twin variants. A general theory of bent and twisted states is given, applicable to both twinning and austenite/martensite transformations. Some of these configurations achieve order-of-magnitude amplification of rotation and axial strain. We investigate also atomistic analogues of these bent and twisted configurations with perfect interfaces between phases. These mechanisms of large deformation, induced by small magnetic fields or temperature changes, have potential application to the development of new actuation technologies for micro-robotic systems.

An influence of the uniaxial strains in one dimensional zigzag ladder (1DZL) on the properties of polarons and bipolarons is considered. It is shown that strain changes all the parameters of the system, in particular, spectrum, existing bands and the masses of charge carriers. Numerical results obtained by taking into an account the Poisson effect clearly indicate that the properties of the (bi)polaronic system can be tuned via strain. Mass of bipolaron can be manipulated by the strain too which in turn leads to the way of tuning Bose–Einstein condensation temperature T{sub BEC} of bipolarons. It is shown that T{sub BEC} of bipolarons in strained 1DZL reasonably correlates with the values of critical temperature of superconductivity of certain perovskites.

In this paper, we study zigzag graphene nanoribbons with edges reconstructed with Stone-Wales defects, by means of an empirical (first-neighbor) tight-binding method, with parameters determined by ab initio calculations of very narrow ribbons. We explore the characteristics of the electronic band...... structure with a focus on the nature of edge states. Edge reconstruction allows the appearance of a new type of edge states. They are dispersive, with nonzero amplitudes in both sublattices; furthermore, the amplitudes have two components that decrease with different decay lengths with the distance from...... the edge; at the Dirac points one of these lengths diverges, whereas the other remains finite, of the order of the lattice parameter. We trace this curious effect to the doubling of the unit cell along the edge, brought about by the edge reconstruction. In the presence of a magnetic field, the zero...

This book, devoted exclusively to symmetry in chemistry and developed in an essentially nonmathematical way, is a must for students and researchers. Topics include symmetry elements and operations, multiple symmetry operations, multiplication tables and point groups, group theory applications, and crystal symmetry. Extensive appendices provide useful tables.

Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.

In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how to get locality by first obtaining reparametrization symmetry, or equivalently, diffeomorphism symmetry. This is the object of the present article.

The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples such as the SO(4) symmetry of the hydrogen atom and the isospin symmetry in nuclei. Two nuclear models, the shell model and the interacting boson model, are reviewed with particular emphasis on their use of group-theoretical techniques.

Graphene nanostructures are potential building blocks for nanoelectronic and spintronic devices. However, the production of monolayer graphene nanostructures with well-defined zigzag edges remains a challenge. In this paper, we report the patterning of monolayer graphene nanostructures with zigzag edges on hexagonal boron nitride (h-BN) substrates by an anisotropic etching technique. We found that hydrogen plasma etching of monolayer graphene on h-BN is highly anisotropic due to the inert and ultra-flat nature of the h-BN surface, resulting in zigzag edge formation. The as-fabricated zigzag-edged monolayer graphene nanoribbons (Z-GNRs) with widths below 30 nm show high carrier mobility and width-dependent energy gaps at liquid helium temperature. These high quality Z-GNRs are thus ideal structures for exploring their valleytronic or spintronic properties.

Graphene nanostructures are potential building blocks for nanoelectronic and spintronic devices. However, the production of monolayer graphene nanostructures with well-defined zigzag edges remains a challenge. In this paper, we report the patterning of monolayer graphene nanostructures with zigzag edges on hexagonal boron nitride (h-BN) substrates by an anisotropic etching technique. We found that hydrogen plasma etching of monolayer graphene on h-BN is highly anisotropic due to the inert and ultra-flat nature of the h-BN surface, resulting in zigzag edge formation. The as-fabricated zigzag-edged monolayer graphene nanoribbons (Z-GNRs) with widths below 30 nm show high carrier mobility and width-dependent energy gaps at liquid helium temperature. These high quality Z-GNRs are thus ideal structures for exploring their valleytronic or spintronic properties.

The paper contains a description of basic regularities in the manifestation of symmetry of human structural organization and its ontogenetic and phylogenetic development. A concept of macrobiocrystalloid with inherent complex symmetry is proposed for the description of the human organism in its integrity. The symmetry can be characterized as two-plane radial (quadrilateral), where the planar symmetry is predominant while the layout of organs of radial symmetry is subordinated to it. Out of the two planes of symmetry (sagittal and horizontal), the sagittal plane is predominant. The symmetry of the chromosome, of the embrio at the early stages of cell cleavage as well as of some organs and systems in their phylogenetic development is described. An hypothesis is postulated that the two-plane symmetry is formed by two mechanisms: a) the impact of morphogenetic fields of the whole crystalloid organism during embriogenesis and, b) genetic mechanisms of the development of chromosomes having two-plane symmetry.

Highly stretchable conductive composite lines with an ordered zigzag structure are prepared. The high stretchability arises from the interpenetrating network between the polymer gel and Ag nanoparticles, as well as the ordered zigzag morphology. Double transfer of the structures in a perpendicular configuration allows for the fabrication of 2D stretchable electrodes. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

By adding nanotwins to Cu, the surface electromigration (EM) slows down. The atomic mobility of the surface step-edges is retarded by the triple points where a twin meets a free surface to form a zigzag-type surface. We observed that EM can alter the zigzag surface structure to optimize the reduction of EM, according to Le Chatelier's principle. Statistically, the optimal alternation is to change an arbitrary (111)/(hkl) zigzag pair to a pair having a very low index (hkl) plane, especially the (200) plane. Using in situ ultrahigh vacuum and high-resolution transmission electron microscopy, we examined the effects of different zigzag surfaces on the rate of EM. The calculated rate of surface EM can be decreased by a factor of ten.By adding nanotwins to Cu, the surface electromigration (EM) slows down. The atomic mobility of the surface step-edges is retarded by the triple points where a twin meets a free surface to form a zigzag-type surface. We observed that EM can alter the zigzag surface structure to optimize the reduction of EM, according to Le Chatelier's principle. Statistically, the optimal alternation is to change an arbitrary (111)/(hkl) zigzag pair to a pair having a very low index (hkl) plane, especially the (200) plane. Using in situ ultrahigh vacuum and high-resolution transmission electron microscopy, we examined the effects of different zigzag surfaces on the rate of EM. The calculated rate of surface EM can be decreased by a factor of ten. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr05418d

Atomic structural models of zigzag-shaped carbon nanotubes (Z-CNTs) were constructed by periodically introducing pentagons and heptagons into pristine CNTs. In terms of formation energies, the Z-CNTs present comparable energetic stabilities to those of the pristine CNTs and are more stable than C60 fullerene. The mechanical properties of these Z-CNTs, including the Young's modulus, intrinsic strength and failure behaviour, were systematically investigated by first-principles computations. Compared with the pristine CNTs with an average Young's modulus of about 1.0 TPa, incorporation of pentagons and heptagons in the Z-CNTs will reduce the average Young's modulus to several hundreds of GPa. Moreover, the computational results also showed that under uniaxial tensile strain, the intrinsic strength and failure strain of the Z-CNTs are also lower than those of the pristine CNTs. Generally, the Young's modulus and intrinsic strength of the Z-CNTs are exponentially inverse to curvature, which can be expressed by simple formulae. In particular, the electronic properties of the armchair Z-CNTs can be tailored by uniaxial tensile strain. It was also found that through applying tensile strain, a semiconductor-metal or metal-semiconductor transition can be triggered. The localized-delocalized partial charge distribution near the Fermi energy for the strained Z-CNTs can explain the semiconductor-metal or metal-semiconductor transition. This significant electromechanical coupling effect suggests the Z-CNTs have potential applications in nanoscale electromechanical sensors and switches.

Half-metallic materials are the prime requisite for future spintronic devices. In present work, the possibility of half-metallic characteristic has been investigated in Li terminated zigzag graphene nanoribbons (ZGNR) using density functional theory. Two different configurations: (i) both edges Li termination (Li-both edges) and (ii) one edge Li termination (Li-one edge), have been examined in the present study. The calculated binding energy (ranging from -3.19 eV to -4.96 eV) confirms that both the considered configurations are energetically viable to obtain. All the considered structures settled in antiferromagnetic ground state which is more stable than that of spin compensated state. Further, it is revealed that upto 100% spin polarization can be achieved (without application of any external electric field) in ZGNR with Li-one edge. Moreover, the observed half-metallicity is found to be independent of the ribbon width and therefore pledges for applications in novel spin filtering devices.

The rules that govern spin exchange interaction in pristine graphene nanostructures are constrained by the bipartite character of the lattice, so that the sign of the exchange is determined by whether magnetic moments are on the same sublattice or not. The synthesis of graphene ribbons with perfect zigzag edges and a fluoranthene group with a pentagon ring, a defect that breaks the bipartite nature of the honeycomb lattice, has been recently demonstrated. Here we address how the electronic and spin properties of these structures are modified by such defects, both for indirect exchange interactions as well as the emergent edge magnetism, studied both with density functional theory and mean-field Hubbard model calculations. In all instances we find that the local breakdown of the bipartite nature at the defect reverts the sign of the otherwise ferromagnetic correlations along the edge, introducing a locally antiferromagnetic intraedge coupling and, for narrow ribbons, also revert the antiferromagnetic interedge interactions that are normally found in pristine ribbons. Our findings show that these pentagon defects are a resource that permits us to engineer the spin exchange interactions in graphene-based nanostructures.

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.

Vibration suppression remains a crucial issue in the design of structures and machines. Recent studies have shown that with the use of metamaterial inspired structures (or metastructures), considerable vibration attenuation can be achieved. Optimization of the internal geometry of metastructures maximizes the suppression performance. Zigzag inserts have been reported to be efficient for vibration attenuation. It has also been reported that the geometric parameters of the inserts affect the vibration suppression performance in a complex manner. In an attempt to find out the most efficient parameters, an optimization study has been conducted on the linear zigzag inserts and is presented here. The research reported in this paper aims at developing an automated method for determining the geometry of zigzag inserts through optimization. This genetic algorithm based optimization process searches for optimal zigzag designs which are properly tuned to suppress vibrations when inserted in a specific host structure (cantilever beam). The inserts adopted in this study consist of a cantilever zigzag structure with a mass attached to its unsupported tip. Numerical simulations are carried out to demonstrate the efficiency of the proposed zigzag optimization approach.

We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.

Full Text Available Abstract: The symmetry principle is described in this paper. The full details are given in the book: J. Rosen, Symmetry in Science: An Introduction to the General Theory (Springer-Verlag, New York, 1995.

Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.

We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)

Full Text Available Tomato is a major crop plant and several mutants have been selected for breeding but also for isolating important genes that regulate flowering and sympodial growth. Besides, current research in developmental biology aims at revealing mechanisms that account for diversity in inflorescence architectures. We therefore found timely to review the current knowledge of the genetic control of flowering in tomato and to integrate the emerging network into modeling attempts. We developped a kinetic model of the tomato inflorescence development where each meristem was represented by its ‘vegetativeness’ (V, reflecting its maturation state towards flower initiation. The model followed simple rules: maturation proceeded continuously at the same rate in every meristem (dV; floral transition and floral commitment occurred at threshold levels of V; lateral meristems were initiated with a gain of V (ΔV relative to the V level of the meristem from which they derived. This last rule created a link between successive meristems and gave to the model its zigzag shape. We next exploited the model to explore the diversity of morphotypes that could be generated by varying dV and ΔV and matched them with existing mutant phenotypes. This approach, focused on the development of the primary inflorescence, allowed us to elaborate on the genetic regulation of the kinetic model of inflorescence development. We propose that the lateral inflorescence meristem fate in tomato is closer to an immature flower meristem than to the inflorescence meristem of Arabidopsis. In the last part of our paper, we extend our thought to spatial regulators that should be integrated in a next step for unraveling the relationships between the different meristems that participate to sympodial growth.

W-symmetry is an extension of conformal symmetry in two dimensions. Since its introduction in 1985, W-symmetry has become one of the central notions in the study of two-dimensional conformal field theory. The mathematical structures that underlie W-symmetry are so-called W-algebras, which are higher-spin extensions of the Virasoro algebra. This book contains a collection of papers on W-symmetry, covering the period from 1985 through 1993. Its main focus is the construction of W-algebras and their representation theory. A recurrent theme is the intimate connection between W-algebras and affine

Highlights: • Expanded Kitaev–Heisenberg model on honeycomb lattice is investigated. • Kitaev interactions between the first or second nearest neighbors are considered. • Phase competition is discussed by energy calculation and Monte Carlo simulation. • Zigzag phase shows a symmetric behavior to the stripy phase. • Zigzag order is extended to the whole parameter range by more interactions. - Abstract: The Kitaev–Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev–Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.

The crystal structure and magnetic properties of the RbMnPO4 zeolite-ABW-type material have been studied by temperature-dependent neutron powder diffraction, low-temperature magnetometry, and heat capacity measurements. RbMnPO4 represents a rare example of a weak ferromagnetic polar material, containing Mn(2+) ions with TN = 4.7 K. The neutron powder diffraction pattern recorded at T = 10 K shows that the compound crystallizes in the chiral and polar monoclinic space group P2(1) (No. 4) with the unit cell parameters: a = 8.94635(9), b = 5.43415(5), and c = 9.10250(8) Å and β = 90.4209(6)°. A close inspection of the crystal structure of RbMnPO4 shows that this material presents two different types of zigzag chains running along the b axis. This is a unique feature among the zeolite-ABW-type materials exhibiting the P2(1) symmetry. At low temperature, RbMnPO4 exhibits a canted antiferromagnetic structure characterized by the propagation vector k1 = 0, resulting in the magnetic symmetry P2(1)'. The magnetic moments lie mostly along the b axis with the ferromagnetic component being in the ac plane. Due to the geometrical frustration present in this system, an intermediate phase appears within the temperature range 4.7-5.1 K characterized by the propagation vector k2 = (kx, 0, kz) with kx/kz ≈ 2. This ratio is reminiscent of the multiferroic phase of the orthorhombic RMnO3 phases (R = rare earth), suggesting that RbMnPO4 could present some multiferroic properties at low temperature. Our density functional calculations confirm the presence of magnetic frustration, which explains this intermediate incommensurate phase. Taking into account the strongest magnetic interactions, we are able to reproduce the magnetic structure observed experimentally at low temperature.

The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic or nonholonomic systems provided that some conditions hold.

This paper presents the study of Gallium and Aluminum doped Nitrogen terminated zigzag Graphene Nano Ribbon (GNR) FET with high-k dielectric. The GNR FET structure has been designed and simulated using Quantumwise Atomistix Toolkit software package. The presented GNR FET with n-type (Nitrogen doped) electrodes and p-type (Gallium or Aluminum doped) scattering region are simulated and analyzed using Density Functional Theory combined with NEGF formalism and Device Density of States (DDOS). The device shows a negative differential resistance phenomenon which can be controlled by the gate of the zigzag GNR FET. It is found that doping of Gallium and Aluminum in scattering region provides higher drain current, higher ION/IOFF and IP/IV ratios as compared to that of Boron doped zigzag GNR FET. The potential applications of the device are in logical, high frequency, and memory devices.

The Kitaev-Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev-Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.

We provide direct experimental evidence that the one-dimensional (1D) to two-dimensional (2D) zigzag transition in a Yukawa cluster exhibits power law behavior. Configurations of a six-particle dusty (complex) plasma confined in a biharmonic potential well are characterized as the well anisotropy is reduced. When the anisotropy is large the particles are in a 1D straight line configuration. As the anisotropy is decreased the cluster undergoes a zigzag transition to a 2D configuration. The measured dependence of cluster width on anisotropy is well described by a power law. A second transition from the zigzag to an elliptical configuration is also observed. The results are in very good agreement with a model for particles interacting through a Yukawa potential.

We investigate the spin-dependent electron transport in single and double normal/ferromagnetic/normal zigzag graphene nanoribbon (NG/FG/NG) junctions.The ferromagnetism in the FG region originates from the spontaneous magnetization of the zigzag graphene nanoribbon.It is shown that when the zigzag-chain number of the ribbon is even and only a single transverse mode is actived,the single NG/FG/NG junction can act as a spin polarizer and/or a spin analyzer because of the valley selection rule and the spin-exchange field in the FG,while the double NG/FG/NG/FG/NG junction exhibits a quantum switching effect,in which the on and the off states switch rapidly by varying the cross angle between two FG magnetizations.Our findings may shed light on the application of magnetized graphene nanoribbons to spintronics devices.

The Refined Zigzag Theory is applied to the modeling of delaminations in laminated composites. The commonly used cohesive zone approach is adapted for use within a continuum mechanics model, and then used to predict the onset and propagation of delamination in five cross-ply composite beams. The resin-rich area between individual composite plies is modeled explicitly using thin, discrete layers with isotropic material properties. A damage model is applied to these resin-rich layers to enable tracking of delamination propagation. The displacement jump across the damaged interfacial resin layer is captured using the zigzag function of the Refined Zigzag Theory. The overall model predicts the initiation of delamination to within 8% compared to experimental results and the load drop after propagation is represented accurately.

The electronic properties and relative stability of zigzag graphene nanoribbons are studied by varying the percentage of hydroxyl radicals for edge saturation using first principle calculations. The passivated structures of zigzag graphene nanoribbon have spin-polarized ground state with antiferromagnetic exchange coupling across the edge and ferromagnetic coupling along the edges. When the edges are specially passivated by hydroxyl, the potentials of spin exchange interaction across the two edges shift accordingly, resulting into a spin-semiconductor. Varying the concentration of hydroxyl groups can alter the maximum magnetization splitting. When the percentage of asymmetrically adsorbed hydroxyl reaches 50%, the magnetization splitting can reach a value as high as 275 meV due to the asymmetrical potential across the nanoribbon edges. These results would favor spintronic device applications based on zigzag graphene nanoribbons.

Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent grav...

The science of complexity studies the behavior and properties of complex systems in nature and human society.Particular interest has been put on their certain simple common properties.Symmetry is one of such properties.Symmetric phenomena can be found in many complex systems.The purpose of this paper is to reveal the internal reason of the symmetry.Using some physical systems and geometric objects,the paper shows that many symmetries are caused by optimization under certain criteria.It has also been revealed that an evolutional process may lead to symmetry.

''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.

A novel passive micromixer, called a trapezoidal-zigzag micromixer (TZM), is reported. A TZM is composed of trapezoidal channels in a zigzag and split-recombine arrangement that enables multiple mixing mechanisms, including splitting-recombining, twisting, transversal flows, vortices, and chaotic...... advection. The effects of geometric parameters of the TZM on mixing performance are systematically investigated by the Taguchi method and numerical simulations in COMSOL Multiphysics. The number of mixing units, the slope angle of the trapezoidal channel, the height of the constriction element...

Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.

The Symmetry Festival is a science and art program series, the most important periodic event (see its history) to bring together scientists, artists, educators and practitioners interested in symmetry (its roots, what is behind, applications, etc.), or in the consequences of its absence.

It is argued that the existence of symmetries may simplify, as in classical mechanics, the solution of optimal control problems. A procedure for obtaining symmetries for the optimal Hamiltonian resulting from the Maximum Principle is given; this avoids the actual calculation of the optimal

In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dila...

For relativistic quantum field theories, we consider Lorentz breaking, spatially homogeneous field configurations or states that evolve in time along a symmetry direction. We dub this situation "spontaneous symmetry probing" (SSP). We mainly focus on internal symmetries, i.e. on symmetries that commute with the Poincare group. We prove that the fluctuations around SSP states have a Lagrangian that is explicitly time independent, and we provide the field space parameterization that makes this manifest. We show that there is always a gapless Goldstone excitation that perturbs the system in the direction of motion in field space. Perhaps more interestingly, we show that if such a direction is part of a non-Abelian group of symmetries, the Goldstone bosons associated with spontaneously broken generators that do not commute with the SSP one acquire a gap, proportional to the SSP state's "speed". We outline possible applications of this formalism to inflationary cosmology.

We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.

Full Text Available Problem statement: Financial time series were usually large in size, unstructured and of
high dimensionality. Since, the illustration of financial time series shape was typically characterized by
a few number of important points. These important points moved in zigzag directions which could
form technical patterns. However, these important points exhibited in different resolutions and difficult
to determine. Approach: In this study, we proposed novel methods of financial time series indexing
by considering their zigzag movement. The methods consist of two major algorithms: first, the
identification of important points, namely the Zigzag-Perceptually Important Points (ZIPs
identification method and next, the indexing method namely Zigzag based M-ary Tree (ZM-Tree to
structure and organize the important points. Results: The errors of the tree building and retrieving
compared to the original time series increased when the important points increased. The dimensionality
reduction using ZM-Tree based on tree pruning and number of retrieved points techniques performed
better when the number of important points increased. Conclusion: Our proposed techniques
illustrated mostly acceptable performance in tree operations and dimensionality reduction comparing
to existing similar technique like Specialize Binary Tree (SB-Tree.

A 1-meter-long trapezoidal Triple-GEM detector with wide readout strips was tested in hadron beams at the Fermilab Test Beam Facility in October 2013. The readout strips have a special zigzag geometry and run along the radial direction with an azimuthal pitch of 1.37 mrad to measure the azimuthal phi-coordinate of incident particles. The zigzag geometry of the readout reduces the required number of electronic channels by a factor of three compared to conventional straight readout strips while preserving good angular resolution. The average crosstalk between zigzag strips is measured to be an acceptable 5.5%. The detection efficiency of the detector is (98.4+-0.2)%. When the non-linearity of the zigzag-strip response is corrected with track information, the angular resolution is measured to be (193+-3) urad, which corresponds to 14% of the angular strip pitch. Multiple Coulomb scattering effects are fully taken into account in the data analysis with the help of a stand-alone Geant4 simulation that estimates in...

Graphical abstract: Density functional molecular calculations of the minimum energy structure of armchair nanoribbons show that they have the same two dimensional structure as graphene and are stable as free standing structures. However, the planar zigzag structure is shown to not be a minimum energy structure having negative vibrational frequencies. The armchair ribbons have small direct band gaps which decrease with ribbon length approaching metallic behavior. The difference in the density of states between the spin up state and down state at the top of the valence level raises the possibility that the ribbons could be ferromagnetic semiconductors. Research highlights: {yields} DFT calculations predict armchair Si ribbons are stable structures but not zigzags. {yields} The band gap and ionization potential are predicted to decrease with ribbon length. {yields} Ribbons having more than 38 Si atoms are predicted to have triplet ground states. {yields} Al and P doped ribbons have the potential to be ferromagnetic semiconductors. - Abstract: The possibility of stable two dimensional armchair and zigzag silicon nanoribbons having the same structure as graphene is examined using Density Functional Theory (DFT). The calculations predict that armchair Si ribbons, but not zigzag ribbons, are stable two dimensional structures. The electronic and magnetic properties of undoped and hole and electron doped armchair Si ribbons are calculated. It is predicted that electron and hole doped Si armchair ribbons have the potential to be ferromagnetic semiconductors.

The substitutional impurities in zigzag edge (10,0) carbon nanotubes have been studied by using first principles calculations. Silicon (Si), gallium (Ga), and arsenic (As) atom have been chosen as semiconductor based-atom for replacing carbon atoms in CNT's surface. The silicon atom changes the energy gap of pristine zigzag (10,0) CNT, it is 0.19 eV more narrow than that of pristine CNT. Geometrically, the silicon atom creates sp3 bond with three adjacent carbon atoms, where the tetrahedral form of its sp3 bond is consisted of free unoccupied state. The silicon atom does not induce magnetism to zigzag CNT. Due to gallium (Ga) and arsenic (As) atom substitution, the zigzag CNT becomes metallic and has magnetic moment of 1 µB. The valance and conduction band are crossed each other, then the energy gap is vanished. The electronic properties of GaAs-doped CNT are dominantly affected by gallium atom and its magnetic properties are dominantly affected by arsenic atom. These results prove that the CNT with desired properties can be obtained with substitutional impurities without any giving structural defect.

Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their structural boundary conditions. Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics. The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges, but direct observation of spin-polarized edge states for zigzag edge topologies--including ZGNRs--has not yet been achieved owing to the limited precision of current top-down approaches. Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement and filtering, and will ultimately add the spin degree of freedom to graphene-based circuitry.

Tomographic-PIV was used to measure the boundary layer transition forced by a zigzag trip. The resulting instantaneous three-dimensional velocity distributions are used to quantitatively visualize the flow structures. They reveal undulating spanwise vortices directly behind the trip, which break up

In this work, we have found that the difference between armchair and zigzag ends of carbon nanotubes (CNTs) does not pertain at close study for individual bonds and thus alternative strategies need to be developed to reach the ultimate goals in selective growth. Based on first-principles simulations, the difference between binding strengths for CNTs of different chirality was investigated using hydrogen dissociation energies at their passivated ends. When all H atoms are removed collectively we find the well-known difference: that armchair bonds are much weaker than zigzag ones, which is typically seen for both CNT ends and graphene edges. However, when individual H atoms are removed we find almost no difference in hydrogen dissociation energies, small difference in bond lengths, which by association means small difference in C-C and M-C binding energies. We show convincingly that the difference in binding energy between armchair and zigzag ends is due to a fragment stabilization effect that is only manifested when all (or several neighbouring) bonds are broken. This is because at armchair ends/edges neighbouring dangling bonds can pair-up to form C≡C triple bonds that constitute a considerable stabilization effect compared to the isolated dangling bonds at zigzag ends/edges. Consequently, in many processes, e.g., catalytic growth where bonds are normally created/broken sequentially, not collectively, the difference between armchair and zigzag ends/edges cannot be used to discriminate growth of one type over the other to achieve chiral selective growth. Strategies are discussed to realize chirality selective growth in the light of the results presented, including addition of C2-fragments to favor armchair tubes.

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate-symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.

This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

Ever since the discovery of graphene, valley symmetry and its control in the material have been a focus of continued studies in relation to valleytronics. Carrier-guiding quasi-one-dimensional (1D) graphene nanoribbons (GNRs) with quantized energy subbands preserving the intrinsic Dirac nature have provided an ideal system to that end. Here, by guiding carriers through dual-gate operation in high-mobility monolayer graphene, we report the realization of quantized conductance in steps of 4e2/h in zero magnetic field, which arises from the full symmetry conservation of quasi-1D ballistic GNRs with effective zigzag-edge conduction. A tight-binding model calculation confirms conductance quantization corresponding to zigzag-edge conduction even for arbitrary GNR orientation. Valley-symmetry conservation is further confirmed by intrinsic conductance interference with a preserved Berry phase of π in a graphene-based Aharonov-Bohm (AB) ring prepared by similar dual gating. This top-down approach for gate-defined carrier guiding in ballistic graphene is of particular relevance in the efforts towards efficient and promising valleytronic applications.

Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.

According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dim Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected SO(n) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an SO(n-1,1) connection on the spacetime. The principal fiber bundle character of the original SO(n) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.

Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

Full Text Available Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

In the literature the $CPT$ theorem has only been established for Hamiltonians that are Hermitian. Here we extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products and invariance under complex Lorentz transformations. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter requirement then forces this antilinear symmetry to be $CPT$, with Hermiticity of a Hamiltonian thus only being a sufficient condition for $CPT$ symmetry and not a necessary one. $CPT$ symmetry thus has primacy over Hermiticity, and it rather than Hermiticity should be taken as a guiding principle for constructing quantum theories. With confo...

Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.

In the present work we consider the relation between superconductivity and spontaneous gauge symmetry breaking (SGBS). We show that ODLRO does not require in principle SBGS, even in the presence of particle number fluctuations, by examining exact solutions of a fermionic pairing model. The criteria become equivalent if a symmetry breaking field is allowed, which can be attributed to the interaction with the environment. However, superconducting states without SBGS are not forbidden.

Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.

This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D{sub 4}, the other describing quarks and employing the symmetry D{sub 14}. In the latter model it is the quark mixing matrix element V{sub ud} - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)

The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.

Zigzag graphene nanoribbons are predicted to exhibit interesting electronic properties stemming from its Dirac band structure. However, to date, investigation of them is highly limited because of the defects and the roughness at the edges, which mix different valley properties of graphene. Here, we report the signature of conservation of valley symmetry in two types of quasi-1D ballistic graphene transport devices; one is a quantum point contact (QPC) and another is an Aharonov-Bohm (AB) interferometer. In measurements, charge carriers were confined in a potential well formed by the dual gates operation and the four-terminal magnetoconductance (MC) was measured with varying the carrier density, dc bias, and temperature. It exhibits the conductance quantization in steps of ΔG = 4e2/ h starting from G = (2, 6), 10 ×e2 / h in a constricted conducting channel of QPC-type devices. This behavior is similar to the one observed in zigzag graphene nanoribbons having edge localized channels. Our tight-binding calculation shows that quasi-1D charge flow on a graphene plane acts a zigzag-type nanoribbon, unless it is perfectly aligned along the armchair direction. In the AB interferometry, we observed h/ e periodic modulation of MC and the zero-field conductance minimum with a negative MC background.

We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic symmetry, different from the space-time supersymmetry and the BRST symmetry. Subsidiary conditions on states guarantee the unitarity of systems.

We theoretically investigate the effect of a transverse electric field generated by side gates and a vertical electric field generated by top/back gates on energy bands and transport properties of zigzag bilayer graphene ribbons (Bernal stacking). Using atomistic tight binding calculations and Green’s function formalism we demonstrate that a bandgap is opened when either field is applied and even enlarged under simultaneous influence of the two fields. Interestingly, although vertical electric fields are widely used to control the bandgap in bilayer graphene, here we show that transverse fields exhibit a more positive effect in terms of modulating a larger range of bandgap and retaining good electrical conductance. The Seebeck effect is also demonstrated to be enhanced strongly—by about 13 times for a zigzag bilayer graphene ribbon with 16 chain lines. These results may motivate new designs of devices made of bilayer graphene ribbons using electric gates.

The electronic properties of silicene zigzag nanoribbons with the presence of perpendicular fields are studied by using first-principles calculations and the generalized nearest neighboring approximation method. In contrast to the planar graphene, in silicene the Si atoms are not coplanar. As a result, by applying perpendicular fields to the two-dimensional silicene sheet, the on-site energy can be modulated and the band gap at the Dirac point is open. The buckled structure also creates a height difference between the two edges of the silicene zigzag nanoribbons. We find that the external fields can modulate the energies of spin-polarized edge states and their corresponding band gaps. Due to the polarization in the plane, the modulation effect is width dependent and becomes much more significant for narrow ribbons.

Graphene quantum dots (GQDs), which are edge-bound nanometer-size graphene pieces, have fascinating electronic and optical properties due to their quantum confinement and edge effect. In this paper, GQDs were synthesized by using acid treatment and chemical exfoliation of multi-walled carbon nanotubes (MWCNTs). The structure of the GQDs was investigated by transmission electron microscope. The GQDs have a uniform size distribution, zigzag edge structure and two-dimensional morphology. The results indicated that the GQDs have bright blue emission upon UV excitation. The highly fluorescent GQDs exhibited high water solubility and good stability. It is shown that the acid treatment of MWCNTs leads to the formation of the functional group in zigzag sites, which results in the pH-dependent fluorescence of the GQDs.

In this manuscript, the formation of nickel nanowires of 10-20 nm in diameter (average size: several tens to hundreds of {mu}m long and 1.0-1.5 {mu}m wide) at low temperature is found to be driven by dewetting of liquid organometallic precursors during spin-coating process and by self-assembly of Ni clusters. Elaboration of metallic thin films by low-temperature deposition technique makes the preparation process compatible with most of the substrates. The use of iron and cobalt precursor shows that the process could be extended to other metallic systems. In this work, AFM and SEM are used to follow the assembly of Ni clusters into straight or zigzag lines. The formation of zigzag structure is specific to the Ni precursor at appropriate preparation parameters. This template-free process allows a control of anisotropic structures with homogeneous sizes and angles on the standard Si/SiO{sub 2} surface.

We have theoretically investigated the electronic and magnetic properties of graphene whose zigzag edges are oxidized. The alteration of these properties by adsorption of $\\mathrm{H_{2}O}$ and $\\mathrm{NH_3}$ molecules have been considered. It was found that the adsorbed molecules form a cluster along the oxidized zigzag edges of graphene due to interaction with the electro-negative oxygen. Graphene tends to donate a charge to the adsorbates through the oxygen atoms and the efficiency of donation depends on the intermolecular distance and on the location of the adsorbed molecules relative to the plane of graphene. It was found that by appropriate selection of the adsorbates, a controllable and gradual growth of $p$-doping in graphene with a variety of adsorbed molecules can be achieved

The magnetic structure and magnetic transport properties of hydrogen-passivated sawtooth zigzag-edge graphene nanoribbons (STGNRs) are investigated theoretically. It is found that all-sized ground-state STGNRs are ferromagnetic and always feature magnetic semiconductor properties, whose spin splitting energy gap E(g) changes periodically with the width of STGNRs. More importantly, for the STGNR based device, the dual spin-filtering effect with the perfect (100%) spin polarization and high-performance dual spin diode effect with a rectification ratio about 10(10) can be predicted. Particularly, a highly effective spin-valve device is likely to be realized, which displays a giant magnetoresistace (MR) approaching 10(10)%, which is three orders magnitude higher than the value predicted based on the zigzag graphene nanoribbons and six orders magnitude higher than previously reported experimental values for the MgO tunnel junction. Our findings suggest that STGNRs might hold a significant promise for developing spintronic devices.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry ene...

In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.

The possible maximal mixing seen in the oscillations of atmospheric neutrinos has led to the postulate of {mu}-{tau} symmetry, which interchanges {nu}{sub {mu}} and {nu}{sub {tau}}. We argue that such a symmetry need not be special to neutrinos but can be extended to all fermions. The assumption that all fermion mass matrices are approximately invariant under the interchange of the second and the third generation fields is shown to be phenomenologically viable and has interesting consequences. In the quark sector, the smallness of V{sub ub} and V{sub cb} can be consequences of this approximate 2-3 symmetry. The same approximate symmetry can simultaneously lead to a large atmospheric mixing angle and can describe the leptonic mixing quite well. We identify two generic scenarios leading to this. One is based on the conventional type-I seesaw mechanism and the other follows from the type-II seesaw model. The latter requires a quasi-degenerate neutrino spectrum for obtaining large atmospheric neutrino mixing in the presence of an approximate {mu}-{tau} symmetry. (orig.)

We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest and next nearest neighboring waveguides exist. It is shown that there is a stop band in the spectrum of linear waves. The system of evolution equations for coupled waves has the steady state solution describing the electromagnetic pulse running in the array. Numerical simulation demonstrates robustness of these solitary waves.

Zig-zag structure of the nickel thin film has been obtained using Glancing Angle Deposition (GLAD) technique. Glass substrate was positioned 75 degrees with respect to the substrate normal. The obtained nickel thin film was characterized by X-ray Photoelectron Spectroscopy, Scanning Electron Microscopy and Atomic Force Microscopy. Surface energy of the deposited thin film was determined by measuring the contact angle using the static sessile drop method. [P...

In this paper, we study the spectra of Schrödinger operators on zigzag carbon nanotubes, which are broken by abrasion or during refining process. Throughout this paper, we assume that the carbon nanotubes are broken periodically and we deal with one of those models. Making use of the Floquet–Bloch theory, we examine the spectra of the Schrödinger operators and compare the spectra of the broken case and the pure unbroken case.

Full Text Available Zig-zag structure of the nickel thin film has been obtained using Glancing Angle Deposition (GLAD technique. Glass substrate was positioned 75 degrees with respect to the substrate normal. The obtained nickel thin film was characterized by X-ray Photoelectron Spectroscopy, Scanning Electron Microscopy and Atomic Force Microscopy. Surface energy of the deposited thin film was determined by measuring the contact angle using the static sessile drop method. [Projekat Ministarstva nauke Republike Srbije, br. III 45005

The zigzag edges of graphene on Ir(111) are studied by ab initio simulations and low-temperature scanning tunneling spectroscopy, providing information about their structural, electronic, and magnetic properties. No edge state is found to exist, which is explained in terms of the interplay between a strong geometrical relaxation at the edge and a hybridization of the d orbitals of Ir atoms with the graphene orbitals at the edge.

Based on first-principles calculations, we have systematically investigated the structural stability, electronic and magnetic properties of zigzag C2N nanoribbons (ZC2NNRs). Different from zigzag graphene nanoribbons (ZGNRs), the ground states of ZC2NNRs present ferromagnetic metal, antiferromagnetic semiconductor and spin semiconductor dependently on the edge configuration and width of nanoribbons. Our results suggest the ZC2NNRs have great potential applications in spintronic, thermoelectric and optoelectronic devices.

A new refined theory for laminated-composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining accurate estimates of structural response of laminated composites.

In this paper, using first principle calculation and non-equilibrium Green's function, the thermally induced spin current in Hydrogen terminated Zigzag-edge Germanene Nanoribbon (ZGeNR-H) is investigated. In this model, because of the difference between the source and the drain temperature of ZGeNR device, the spin up and spin down currents flow in the opposite direction with two different threshold temperatures (Tth). Hence, a pure spin polarized current which belongs to spin down is obtained. It is shown that, for temperatures above the threshold temperature spin down current increases with the increasing temperature up to 75 K and then decreases. But spin up current rises steadily and in the high temperature we can obtain polarized spin up current. In addition, we show an acceptable spin current around the room temperature for ZGeNR. The transmission peaks in ZGeNR which are closer to the Fermi level rather than Zigzag Graphene Nanoribbon (ZGNRS) which causes ZGeNR to have spin current at higher temperatures. Finally, it is indicated that by tuning the back gate voltage, the spin current can be completely modulated and polarized. Simulation results verify the Zigzag Germanene Nanoribbon as a promising candidate for spin caloritronics devices, which can be applied in future low power consumption technology.

This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...

Seeing Through Symmetry is a course that introduces non-science majors to the pervasive influence of symmetry in science. The concept of symmetry is usedboth as a link between subjects (such as physics, biology, mathematics, music, poetry, and art) and as a method within a subject. This is done through the development and use of interactive multimedia learning environments to stimulate learning. Computer-based labs enable the student to further explore the concept by being gently led from the arts to science. This talk is an update that includes some of the latest changes to the course. Explanations are given on methodology and how a variety of interactive multimedia tools contribute to both the lecture and lab portion of the course (created in 1991 and taught almost every semester since then, including one in Sweden).

A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibb...

and evaluate the method. The method uses deformable registration on computed tomography(CT) to find anatomical symmetry deviations of Head & Neck squamous cell carcinoma and combining it with positron emission tomography (PET) images. The method allows the use anatomical and symmetrical information of CT scans...... to improve automatic delineations. Materials: PET/CT scans from 30 patients were used for this study, 20 without cancer in hypopharyngeal volume and 10 with hypharyngeal carcinoma. An head and neck atlas was created from the 20 normal patients. The atlas was created using affine and non-rigid registration...... of the CT-scans into a single atlas. Afterwards the standard deviation of anatomical symmetry for the 20 normal patients was evaluated using non-rigid registration and registered onto the atlas to create an atlas for normal anatomical symmetry deviation. The same non-rigid registration was used on the 10...

Research publications concerning managers who coach their own employees are barely visible despite its wide- spread use in enterprises (McCarthy & Milner, 2013; Gregory & Levy, 2011; Crabb, 2011). This article focuses on leadership, power and moments of symmetry in the coaching relationship...... session. Thereafter we executed qualitative interviews with both managers and employees. Subsequently, a Thematic Analysis resulted in several themes, including power and moments of symmetry in the coaching relationship. One main conclusion is that the most fruitful coaching was obtained when the coachee...... experienced moments of symmetry and that necessary and sufficient conditions to bring forth such moments include a strong working alliance and the coach being aware of the power at play....

The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.

The nuclear equation-of-state is a topic of highest current interest in nuclear structure and reactions as well as in astrophysics. In particular, the equation-of-state of asymmetric matter and the symmetry energy representing the difference between the energy densities of neutron matter and of symmetric nuclear matter are not sufficiently well constrained at present. The density dependence of the symmetry energy is conventionally expressed in the form of the slope parameter L describing the derivative with respect to density of the symmetry energy at saturation. Results deduced from nuclear structure and heavy-ion reaction data are distributed around a mean value L=60 MeV. Recent studies have more thoroughly investigated the density range that a particular observable is predominantly sensitive to. Two thirds of the saturation density is a value typical for the information contained in nuclear-structure data. Higher values exceeding saturation have been shown to be probed with meson production and collective ...

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation does not present duality symmetry, there is a particular theory in which this symmetry is present. This theory is a self dual (or anti-self dual) teleparallel gravity in which, owing to the fact that it does not contribute to the gravitational interaction of fermions, the purely tensor part of torsion is assumed to vanish. The corresponding fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory will probably be much more amenable to renormalization than teleparallel gravity or general relativity. Although obtained in the context of teleparallel gravity, these results must also be true for general relativity.

We consider a new approach to fermion masses and mixings in which no special 'horizontal' dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.

In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational

Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.

The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $\\pi N \\sigma$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.

We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.

The role of isospin asymmetry in nuclei and neutron stars is discussed, with an emphasis on the density dependence of the nuclear symmetry energy. Results obtained with the self-consistent Green function method are presented and compared with various other theoretical predictions. Implications for t

One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.

One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also underst...

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also unders...

Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)

The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued 1-form gauge fields so as to lift the symmetry to Maps(Sigma,G). Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields v_a on the target M satisfying the extended Killing equation v_{a(i;j)}=0 for some connection acting on the index a. For regular foliations this is equivalent to merely requiring the distribution orthogonal to the leaves to be invariant with respect to leaf...

While symmetry and impartiality have become ruling principles in S&TS, defining its core ideal of a 'value-free relativism', their philosophical anchorage has attracted much less discussion than the issue or:how far their jurisdiction can be extended or generalized. This paper seeks to argue that sy

I discuss several topics in the applications of chiral symmetry at nonzero temperature, including: where the rho goes, disoriented chiral condensates, and the phase diagram for QCD with 2+1 flavors. (Based upon talks presented at the "Workshop on Finite Temperature QCD", Wuhan, P.R.C., April, 1994.)

Omnibus tests for central symmetry of a bivariate probability distribution are proposed. The test statistics compare empirical measures of opposite regions. Under rather weak conditions, we establish the asymptotic distribution of the test statistics under the null hypothesis; it follows that they a

We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the \\Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.

We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.

We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.

We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...

The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D a...

We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a system with or without the time reversal invariance. An interpolating formula for the case of gradual time reversal symmetry breaking is proposed.

Maximal Entanglement appears to be a key ingredient for the emergence of symmetries. We first illustrate this phenomenon using two examples: the emergence of conformal symmetry in condensed matter systems and the relation of tensor networks to holography. We further present a Principle of Maximal Entanglement that seems to dictate to a large extend the structure of gauge symmetry.

regarding managers coaching their employees and it is asked; what contributes to coaching of high quality when one reflects on the power aspect as being immanent? Fourteen middle managers coached five of their employees, and all members of each party wrote down cues and experiences immediately after each......Research publications concerning managers who coach their own employees are barely visible despite its wide- spread use in enterprises (McCarthy & Milner, 2013; Gregory & Levy, 2011; Crabb, 2011). This article focuses on leadership, power and moments of symmetry in the coaching relationship...... session. Thereafter we executed qualitative interviews with both managers and employees. Subsequently, a Thematic Analysis resulted in several themes, including power and moments of symmetry in the coaching relationship. One main conclusion is that the most fruitful coaching was obtained when the coachee...

Full Text Available Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion and symmetric opposition (sinusoidal waves are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition. These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series. The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.

When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. In fact, modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. It is shown that the Universe cannot possess exact symmetry, which is a principle of fundamental significance. Curie's principle - which states that the symmetry of the effect is at least that of the cause - features prominently. An introduction to group theory, the mathematical language of symmetry, is included. This book will convince all interested readers of the importance of symmetry in science. Furthermore, it will serve as valuable background reading for all students in the physical sciences.

The edge reconstruction effect of the zigzag silicon carbide nanoribbons (zz SiC NRs) to a stable line of alternatively fused seven and five membered rings without and with H passivation have been studied using first principles density functional theory (DFT). The both side's edges of the pristine SiC are respectively terminated by Si and C atoms and are called the Si-edge and the C-edge, respectively. In the un-passivated systems, the C-edge reconstructed (Crc) could effectively lower the edge energy of the system, while the Si-edge reconstructed (Sirc) could raise the edge energy of the system. Thus, the Crc edge is the best edge for the edge reconstruction of the system, while the both edge reconstructed (brc) system is the metastability. Moreover, the brc system has a nonmagnetic metallic state, whereas the Crc system, as well as Sirc system, has a ferromagnetic metallic state. The edge reconstructed destroys the magnetic moment of the corresponding edge atoms. The magnetic moment arises from the unreconstructed zigzag edges. The pristine zz edge system has a ferrimagnetic metallic state. However, in the H-passivated systems, the unreconstructed zigzag edge (zz-H) is the best edge. The Crc-H system is the metastability. The Sirc-H system has only slightly higher energy than the Crc-H system, whereas the brc-H system of the pristine SiC NR has the highest edge energy. Thus, the H passivation would prevent the occurrence of edge reconstruction. Moreover, H passivation induces a metal-semiconductor transition in the zz and brc SiC NRs. Additionally, except for brc-H system which has non-magnetic semiconducting state, the zz-H, Crc-H, and Sirc-H systems have the magnetic state.

way to choose among them. Spirals can occur in natural figures, e.g. a spiralled tail or a coil of rope or vine tendril, and in line drawings. Since...generated and removes it and all regions similar to it from the list of regions. The end result is a pruned list of distinct optimal regions. 4.7...that, at least to a first approximation, the potential symmetry regions pruned by the locality restriction are not perceptually salient. For example

This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.

The symmetry issue for Galileons has been studied. In particular we address scaling (conformal) and Noether symmetrized Galileons. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been made on Galileons. We have been proven that for Galileons always is possible to find a way to "symmetrized" Galileo's field .

PHYSICAL REVIEW A 87, 012103 (2013) Invisibility and PT symmetry Ali Mostafazadeh* Department of Mathematics, Koc¸ University, Sarıyer 34450, Istanbul, Turkey (Received 9 July 2012; published 3 January 2013) For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT ) transformation. We determine the PT -symmetric as well as no...

Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.

Top-down subtractive lithography has previously been used to pattern graphene nanostructures which lack ideal properties due to (1) limited resolution and (2) disordered edges. Here, we introduce a method to convert such disordered edges into relatively smooth zigzag edges via annealing on a Cu(111) substrate at ~950 °C. The Cu catalyzes the re-arrangement of graphene edge atoms to energetically favorable sites, inducing zigzag edge faceting. The dimensions of the graphene nanostructures can be increased, decreased, or held constant during the annealing by tuning the relative balance between growth and etching reactions, described by a fundamental growth rate equation. To demonstrate the flexibility of this method, we lithographically pattern graphene nanoribbons with zigzag or armchair orientations, or alternatively perforate graphene with circular holes, and then anneal these nanostructures to realize zigzag edge termination in each case, with nanostructure feature size tailored from 8 to 80 nm. The annealed nanostructures have smoother zigzag edges (~40% reduction in 1σ line edge roughness), and Raman spectroscopy confirms that they have lower edge disorder than top-down patterned samples.

This article presents an experimental investigation on the heat transfer performance and pressure drop characteristic of two types of nanofluids flowing through microchannel heat sink with multiple zigzag flow channel structures (MZMCHS). SiO2 nanoparticles dispersed in DI water with concentrations of 0.3 and 0.6 vol.% were used as working fluid. MZMCHS made from copper material with dimension of 28 × 33 mm. Hydraulic diameter of MZMCHs is designed at 1 mm, 7 number of flow channels and heat ...

The one-dimensional hybrid structures of C36 encapsulated in zigzag single-wall carbon nanotubes (C36@(n,0)) have been investigated using ab initio self-consistent-field crystal orbital method based on the density functional theory. The research focuses on the change of geometric and band structures for the nanotubes upon C36 encapsulation. The obtained results show that the introduction of C36 can modify the electronic properties of CNT. The diameter of carbon nanotube plays an important role in the geometric and electronic properties of the peapod structures.

First-principles pseudopotential-based density functional theory calculations of atomic and electronic structures, full phonon dispersions and thermal properties of zigzag single wall carbon nanotubes (SWCNTs) are presented. By determining the correlation between vibrational modes of a graphene sheet and of the nanotube, we understand how rolling of the sheet results in mixing between modes and changes in vibrational spectrum of graphene. We find that the radial breathing mode softens with decreasing curvature. We estimate thermal expansion coefficient of nanotubes within a quasiharmonic approximation and identify the modes that dominate thermal expansion of some of these SWCNTs both at low and high temperatures.

The structural and mechanical properties of graphene nanoribbons (GNRs) under uniaxial tensile strain are studied by density functional theory. The ideal strength of a zigzag GNR (120 GPa) is close to that of pristine graphene. However, for a GNR with both edges reconstructed to pentagon–heptagon pairs (from hexagon–hexagon pairs) it decreases to 94 GPa and the maximum tensile strain is reduced to 15%. Our results constitute a comprehensive picture of the edge structure effect on the mechanical properties of GNRs.

The effect of vacancies on the robustness of zero-energy edge electronic states in zigzag-type graphene layer is studied at different concentrations and distributions of defects. All calculations are performed by using the Green's function method and the tight-binding approximation. It is found that the arrangement of defects plays a crucial role in the destruction of the edge states. We have specified a critical distance between edge vacancies when their mutual influence becomes significant and affects markedly the density of electronic states at graphene edge.

@@ Spin-filter effect is predicted in a weak coupled junction composed of a nonmagnetic metal electrode and a zigzag carbon nanotube. This effect is induced by the magnetic edge states of the nanotube, and can produce spinpolarized current in the absence of an external magnetic field. We find that the spin polarization of the current changes its sign at the half-filling point of the nanotube, thus electric field control of spin transport can be realized. Furthermore, we find the coupling strength of the junction may cause a magnetic transition on the edge of the nanotube.

Through the Green's function formalism and tight-binding Hamiltonian model calculations, the temperature dependent electronic thermal conductivity (TC) for different diameters of zigzag carbon nanotubes and their corresponding unzipped armchair graphene nanoribbons is calculated. All functional temperature dependencies bear crossovers, for which, at higher temperatures, nanotubes have a slightly higher TC than their derived nanoribbons, while below that crossover, both systems exhibit a significant coincidence over a moderate range of lower temperatures. Noticeably, TC decreases with increasing the width or diameter of the corresponding systems. Also, at low temperatures TC is proportional to the density of states around the Fermi level, and thus increasing for metal or semiconductors of narrower gap cases.

We investigate the electronic and magnetic properties of the corrugated zigzag graphene nanoribbons (ZGNRs) with divacancy defects by means of the first principle calculations. We show that the magnitude of corrugation in the defective ZGNR determines whether the system is in the antiferromagnetic state, in the ferromagnetic state, or in the nonmagnetic state. Correspondingly, the mutual transition between the semiconductor and the metal can also be realized in this structure. Moreover, for semiconductors the energy gap displays oscillating behaviors as the magnitude of corrugation increases. These results are identified as being useful in manufacturing flexible devices.

Full Text Available By performing first-principle quantum transport calculation, the spin-dependent transport properties of zigzag-edged bilayer graphene nanoribbon based devices are investigated. There are four kinds of structures with different stacking sequences and treatment of dangling bonds considered in our work. It is shown that the devices are perfect spin-filters with extremely large spin polarization as well as substantial negative differential resistance effects, which are affected by the stacking sequences and edge structures. All these phenomena can be explained by the spin-resolved local density of states and the tranmission spectra.

Using first principle calculation, we investigate the structural, electronic and magnetic properties of silicon doped zigzag boron nitride nanoribbon (ZBNNR). Our results show that the shift in position of silicon doping with respect to the ribbon edge causes change in the structural geometry, electronic structure and magnetization of ZBNNR. The band gap of silicon doped ZBNNR is found to become narrower as compared to that of perfect ZBNNR. We find that band gap and magnetic moment of ZBNNR can be tuned by substitutional silicon doping position and doping concentration.

Based on the Huygens-Fresnel principle, we design a planar lens to efficiently realize the interconversion between the point-like sound source and Gaussian beam in ambient air. The lens is constructed by a planar plate perforated elaborately with a nonuniform array of zigzag slits, where the slit exits act as subwavelength-sized secondary sources carrying desired sound responses. The experiments operated at audible regime agree well with the theoretical predictions. This compact device could be useful in daily life applications, such as for medical and detection purposes.

We study spin-orbit torques and charge pumping in magnetic quasi-one-dimensional zigzag nanoribbons with a hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences a topological phase transition from a trivial band insulator to a quantum spin Hall insulator by tuning of either the magnetization direction or the intrinsic spin-orbit coupling. We find that the spin-charge conversion efficiency (i.e., spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.

We show theoretically that pure spin current can be generated in zigzag edged graphene nanoribbons through the adiabatic pumping by edge selective pumping potentials. The origin of such pure spin current is the spin splitting of the edge localized states, which are oppositely spin polarized at opposite edges. In the proposed device, each edge of the ribbon is covered by two independent time-periodic local gate potentials with a definite phase difference, inducing the edge spin polarized current. When the pumping phase difference is opposite in sign between two edges, the total charge currents is zero and the pure edge spin current is generated.

Based on the Huygens-Fresnel principle we design a planar lens to efficiently realize the interconversion of the point-like source and Gaussian beam in the air ambience. The lens is constructed by a planar plate drilled elaborately with a nonuniform array of zigzag slits, where the slit exits act as subwavelength-sized secondary sources carrying desired sound responses. The experiments operated at audible regime agree well with the theoretical predictions. This compact device could be useful in daily life applications, such as for medical and detection purposes.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

Full Text Available The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D and 3D perception analyses. We start analyzing a pair of twin buildings with projection of the architectural composition elements in 2D picture plane (plane of the composition and we distinguish four 2D keyframe cases based on the relation between the bilateral symmetry of the twin composition and the bilateral symmetry of each element. In 3D perception for each 2D keyframe case there are two sub-variants, with and without a symmetry plane parallel to the picture plane. The bilateral symmetry is dominant if the corresponding symmetry plane is orthogonal to the picture plane. The essence of the complete classification is relation between the bilateral (dominant symmetry of the architectural composition and the bilateral symmetry of each element of that composition.

Calculations have been made for single-walled zigzag (n, 0) carbon nanotubes containing substitutional boron impurity atoms using ab initio density functional theory. It is found that the formation energies of these nanotubes depend on the tube diameter, as do the electronic properties, and show periodic fea-ture that results from their different π bonding structures compared to those of perfect zigzag carbon nanotubes. When more boron atoms are incorporated into a single-walled zigzag carbon nanotube, the substitutional boron atoms tend to come together to form structure of BC3 nanodomains, and B-doped tubes have striking acceptor states above the top of the valence bands. For the structure of BC3, there are two kinds of configurations with different electronic structures.

Calculations have been made for single-walled zigzag(n,0) carbon nanotubes containing substitutional boron impurity atoms using ab initio density functional theory.It is found that the formation energies of these nanotubes depend on the tube diameter,as do the electronic properties,and show periodic fea-ture that results from their different π bonding structures compared to those of perfect zigzag carbon nanotubes.When more boron atoms are incorporated into a single-walled zigzag carbon nanotube,the substitutional boron atoms tend to come together to form structure of BC3 nanodomains,and B-doped tubes have striking acceptor states above the top of the valence bands.For the structure of BC3,there are two kinds of configurations with different electronic structures.

The pursuit of controlled magnetism in semiconductors has been a persisting goal in condensed matter physics. Recently, Vene (phosphorene, arsenene and antimonene) has been predicted as a new class of 2D-semiconductor with suitable band gap and high carrier mobility. In this work, we investigate the edge magnetism in zigzag puckered Vene nanoribbons (ZVNRs) based on the density functional theory. The band structures of ZVNRs show half-filled bands crossing the Fermi level at the midpoint of reciprocal lattice vectors, indicating a strong Peierls instability. To remove this instability, we consider two different mechanisms, namely, spin density wave (SDW) caused by electron-electron interaction and charge density wave (CDW) caused by electron-phonon coupling. We have found that an antiferromagnetic Mott-insulating state defined by SDW is the ground state of ZVNRs. In particular, SDW in ZVNRs displays several surprising characteristics:1) comparing with other nanoribbon systems, their magnetic moments are antiparallelly arranged at each zigzag edge and almost independent on the width of nanoribbons; 2) comparing with other SDW systems, its magnetic moments and band gap of SDW are unexpectedly large, indicating a higher SDW transition temperature in ZVNRs; 3) SDW can be effectively modified by strains and charge doping, which indicates that ZVNRs have bright prospects in nanoelectronic device.

We performed density functional theory study on electronic structure, magnetic properties and stability of zigzag MoS{sub 2} nanoribbons (ZMoS{sub 2}NRs) with and without oxygen (O) passivation. The bare ZMoS{sub 2}NRs are magnetic metal with ferromagnetic edge states, edge passivation decreases their magnetism because of the decrease of edge unsaturated electrons. Obviously, the electronic structure and magnetic properties of ZMoS{sub 2}NRs greatly depend on edge states. When both edges are passivated by O atoms, ZMoS{sub 2}NRs are nonmagnetic metals. When either edge is passivated by O atoms, the systems exhibit single-edge ferromagnetism and magnetism concentrates on the non-passivated edge. Edge passivation can not only tune the magnetism of ZMoS{sub 2}NRs, but also enhance their stability by eliminating dangling bonds. These interesting findings on ZMoS{sub 2}NRs may open the possibility of their application in nanodevices and spintronics. - Highlights: • Edge passivation for tuning magnetism of zigzag MoS{sub 2} nanoribbons (ZMoS{sub 2}NRs) is proposed. • Edge passivation can tune ZMoS{sub 2}NRs from nonmagnetic metal to ferromagnetic metal. • When either edge is passivated, the systems exhibit single-edge ferromagnetic states. • These findings may inspire great interest in the community of ZMoS{sub 2}NRs and motivate numerous experimental researches.

Layered structures of molybdenum disulfide (MoS2) belong to a new class of two-dimensional (2D) semiconductor materials in which monolayers exhibit a direct band gap in their electronic spectrum. This band gap has recently been shown to vanish due to the presence of metallic edge modes when MoS2 monolayers are terminated by zigzag edges on both sides. Here, we demonstrate that a zigzag nanoribbon of MoS2, when exposed to an external exchange field in combination with a transverse electric field, has the potential to exhibit a peculiar half-metallic nature and thereby allows electrons of only one spin direction to move. The peculiarity of such spin-selective conductors originates from a spin switch near the gap-closing region, so the allowed spin orientation can be controlled by means of an external gate voltage. It is shown that the induced half-metallic phase is resistant to random fluctuations of the exchange field as well as the presence of edge vacancies.

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B> = *. The formal parrallelism breaks down at the level of interpretation because (A|C) = ||2. CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is = = , with |Φ> denoting a preparation, |Ψ> a measurement, and U the evolution operator. The transformation |Ψ> = |UΦ> or |Φ> = |U-1Ψ> exchanges the “preparation representation” and the “measurement representation” of a system and is ancillary in the formalization of the quantum chance game by the “wavelike algebra” of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude = Σ between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility = * implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of “blind statistical retrodiction”—that is, of “final cause.”

First-principles calculations are performed for electron transmission through a metallic zigzag carbon nanotube with substitutional BN dimers parallel to the nanotube axis. The transmission coefficient is calculated in the energy range (around the charge neutrality point) in which there exist two degenerate subbands for each spin. Wave functions in the circumferential direction of one of the degenerate subbands can be chosen so as to have nodes at the position of a carbon dimer parallel to the nanotube axis. It is shown that the transmission probability of an incident wave with such wave-function nodes depends crucially on positions of BN dimers relative to the nodes. By placing each of dimers at one of the nodes, the transmission probability is substantially enhanced and is well described by the Born approximation in spite of spatially extended scattering potential due to ionized B and N. This suggests that the arrangement in the circumferential direction of various impurities influences transport through metallic zigzag carbon nanotubes.

We propose versatile materials based on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a zigzag silicene nanoribbon (ZSNR) on half filling in the presence of an out-of-plane electric field. We show that the topological phase transition in the band dispersion of ZSNR can be probed by using the RKKY interaction. We find that, due to the zero-energy edge states of the ZSNR, the exchange coupling is significantly enhanced when the impurities are located on the zigzag edges, and also explore that the strength of the interaction in the topological insulator phase is much greater than that when the system is in the band insulator region. We present a model to investigate the phase of a system of two magnetic impurities located on the edge of the ZSNR and find that three different magnetic phases, spiral, ferromagnetic, and antiferromagnetic, are possible for different values of the electric field. This electrical tunability of the magnetic phases in silicene can be explored by using current experimental techniques and can be of interest in the field of spintronics.

We present an analytical effective theory for the magnetic phase diagram for zigzag-edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter U. We show that the edge magnetic moment varies as lnU and uncover its dependence on the width W of the ribbon. The physics of this owes its origin to the sensory-organ-like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first-order magnetic transition from an antiparallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag-edge terminated nanostructures such as nanodots. Furthermore, we perform first-principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons.

Structural, electronic, and electrical responses of the H-capped (6,0) zigzag single-walled aluminum nitride nanotube was studied under the parallel and transverse electric fields with strengths 0-140 × 10(-4) a.u. by using density functional calculations. Geometry optimizations were carried out at the B3LYP/6-31G* level of theory using a locally modified version of the GAMESS electronic structure program. The dipole moments, atomic charge variations, and total energy of the (6,0) zigzag AlNNT show increases with increase in the applied external electric field strengths. The length, tip diameters, electronic spatial extent, and molecular volume of the nanotube do not significantly change with increasing electric field strength. The energy gap of the nanotube decreases with increases of the electric field strength and its reactivity is increased. Increase of the ionization potential, electron affinity, chemical potential, electrophilicity, and HOMO and LUMO in the nanotube with increase of the applied parallel electric field strengths shows that the parallel field has a much stronger interaction with the nanotube with respect to the transverse electric field strengths. Analysis of the parameters indicates that the properties of AlNNTs can be controlled by the proper external electric field.

Mobius graphene nanoribbons have only one edge topologically. How the magnetic structures, previously associated with the two edges of zigzag-edged flat nanoribbons or cyclic nanorings, would change for their Mobius counterparts is an intriguing question. Using spin-polarized density functional theory, we shed light on this question. We examine spin states of zigzag-edged Mobius graphene nanoribbons (ZMGNRs) with different widths and lengths. We find a triplet ground state for a Mobius cyclacene, while the corresponding two-edged cyclacene has an open-shell singlet ground state. For wider ZMGNRs, the total magnetization of the ground state is found to increase with the ribbon length. For example, a quintet ground state is found for a ZMGNR. Local magnetic moments on the edge carbon atoms form domains of majority and minor spins along the edge. Spins at the domain boundaries are found to be frustrated. Our findings show that the Mobius topology (i.e., only one edge) causes ZMGNRs to favor one spin over the oth...

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other. This result generalises de Finetti's classical representation theorem for infinitely exchangeable sequences of random variables as well as its quantum-mechanical analogue. It has applications in various areas of physics as well as information theory and cryptography. For example, in experimental physics, one typically collects data by running a certain experiment many times, assuming that the individual runs are mutually independent. Our result can be used to justify this assumption.

This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

Mirror symmetry has undergone dramatic progress during the last five years. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics.

The effect of size of a cooling laser beam in a zig-zag atomic beam collimator on transverse cooling of a krypton atomic beam is investigated. The simulation results show that discreteness in the interaction between the cooling laser beam and atomic beam, arising due to finite size and incidence angle of the cooling laser beam, significantly reduces the value of transverse velocity capture range of the collimator. The experimental observations show the trend similar to that obtained from simulations. Our study can be particularly useful where a small zig-zag collimator is required.

@@ A novel fibre-coupling zig-zag beam deflection technology is developed to investigate the attenuation process of laser-induced shock waves in air. Utilizing ordinal reflections of probe beams by a pair of parallel mirrors,a zig-zag beam field is formed, which has eleven probe beams in the horizontal plane. When a laser-induced shock wave propagates through the testing field, it causes eleven deflection signals one after another. The whole attenuation process of the shock wave in air can be detected and illuminated clearly on one experimental curve.

Full Text Available Despite the emergence of a 125 GeV Higgs-like particle at the LHC, we explore the possibility of dynamical electroweak symmetry breaking by strong Yukawa coupling of very heavy new chiral quarks Q . Taking the 125 GeV object to be a dilaton with suppressed couplings, we note that the Goldstone bosons G exist as longitudinal modes V L of the weak bosons and would couple to Q with Yukawa coupling λ Q . With m Q ≳ 700 GeV from LHC, the strong λ Q ≳ 4 could lead to deeply bound Q Q ¯ states. We postulate that the leading “collapsed state,” the color-singlet (heavy isotriplet, pseudoscalar Q Q ¯ meson π 1 , is G itself, and a gap equation without Higgs is constructed. Dynamical symmetry breaking is affected via strong λ Q , generating m Q while self-consistently justifying treating G as massless in the loop, hence, “bootstrap,” Solving such a gap equation, we find that m Q should be several TeV, or λ Q ≳ 4 π , and would become much heavier if there is a light Higgs boson. For such heavy chiral quarks, we find analogy with the π − N system, by which we conjecture the possible annihilation phenomena of Q Q ¯ → n V L with high multiplicity, the search of which might be aided by Yukawa-bound Q Q ¯ resonances.

Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.

Full Text Available In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.

The notion of a particle-like state emerging from a symmetry breaking is given five corresponding pictures. We start from a geometrical picture in two dimensions involving a modular curve constructed using 336 triangles. The same number of building blocks is found again, this time as 336 contact points in the ten dimensional space of super string theory in the context of the largest kissing number of lattice sphere packing. The next corresponding representation is an abstract one pertinent to the order of the simple linear Lie group SL(2, n) in seven dimensions (n = 7) which leads to 336 symmetries. Subsequently a tensorial picture is given using the Riemannian tensor of relativity theory but this time in an eight dimensional space (n = 8) for which the number of independent components is again 336. Finally we use a physical string theory related picture in the 12 dimensions of F theory to find 336 moduli space dimensions representing the instanton cells of our theory. It is evident that the five preceding pictures are ten fold interconnected and exchangeable. This additional mental freedom does not only enhance the feeling of understanding, but also facilitates the easy recognition of complex mathematical relations and its connection to the physical concepts.

Symmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network (WTN) has been rarely studied so far. In this paper, the authors systematically explore the symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.

Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world (8 pages) Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).

This book successfully combines a thorough treatment of molecular and crystalline symmetry with a simple and informal writing style. By means of familiar examples the author helps to provide the reader with those conceptual tools necessary for the development of a clear understanding of what are often regarded as 'difficult' topics. Christopher Hammond, University of Leeds This book should tell you everything you need to know about crystal and molecular symmetry. Ladd adopts an integrated approach so that the relationships between crystal symmetry, molecular symmetry and features of chemical interest are maintained and reinforced. The theoretical aspects of bonding and symmetry are also well represented, as are symmetry-dependent physical properties and the applications of group theory. The comprehensive coverage will make this book a valuable resource for a broad range of readers.

This new edition of Prof. Strocchi's well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit in terms of the delocalized Coulomb dynamics. Furthermore, the chapter on the Higgs mechanism has been significantly expanded with a non-perturbative treatment of the Higgs phenomenon, at the basis of the standard model of particle physics, in the local and in the Coulomb gauges. Last but not least, a subject index has been added and a number of misprints have been corrected. From the reviews of the first edition: The notion of spontaneous symmetry breaking has proven extremely valuable, the problem is that most derivations are perturbative and heuristic. Yet mathematically precise versions do exist, but are not widely known. It is precisely the aim of his book to correct this unbalance. - It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced, a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. It can be recommended to physicists as well and, of course, for physics/mathematics libraries. J.-P. Antoine, Physicalia 28/2, 2006 Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the non-symmetric ground states and the infinite extension of the system. It is written in a pleasant style at a level suitable for graduate students in

We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.

We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.

This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violat...

This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.

The Conservation of Orbital Symmetry examines the principle of conservation of orbital symmetry and its use. The central content of the principle was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbital symmetry is conserved in concerted reaction. This principle is expected to endure, whatever the language in which it may be couched, or whatever greater precision may be developed in its application and extension. The book ope

We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric symmetries. The induced nontrivial isomorphisms lift and provide new symmetries at the level of Gromov-Witten Theory and Donaldson-Thomas Theory. The polytopes of the toric varieties in question include the permutohedron, the cyclohedron, the associahedron, and in fact all graph associahedra, among others.

Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and then we obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.

We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z{sub 2} in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S{sub 4} flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.

Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.

Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.

We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.

"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...

Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension G{sub max}=U(1){sub B−L}×U(1){sub L{sub e−L{sub μ}}}×U(1){sub L{sub μ−L{sub τ}}}. Simple U(1) subgroups of G{sub max} can be used to impose structure on the righthanded neutrino mass matrix, which then propagates to the active neutrino mass matrix via the seesaw mechanism. We show how this framework can be used to gauge the approximate lepton-number symmetries behind the normal, inverted, and quasidegenerate neutrino mass spectrum, and also how to generate texture-zeros and vanishing minors in the neutrino mass matrix, leading to testable relations among mixing parameters.

We study bosonization in 2 +1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an O (2 )-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a "chiral" mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.

Through first-principles calculations using the nonequilibrium Green's function formalism together with density functional theory, we study the conductance of double-vacancy zigzag graphene nanoribbons doped with four transition metal atoms Ti, V, Cr and Fe. We show that Ti doping induces large spin-filtering with an efficiency in excess of 90% for bias voltages below 0.5 V, while the other metal adatoms do not induce large spin filtering. This is despite the fact that the Ti dopant possesses small spin moment, while large moments reside on V, Cr and Fe dopants. Our analysis shows that the suppression of transmission in the spin-down channel in the Ti-doped graphene nanoribbon, thus the large spin filtering efficiency, is due to transmission anti-resonance arising from destructive quantum interference. These findings suggest that the decoration of graphene with titanium, and possibly other transition metals, can act as effective spin filters for nanospintronic applications.

Full Text Available The very brittle oxygen ion conductor yttria stabilized zirconia (YSZ is a typical solid electrolyte for miniaturized thin film fuel cells. In order to decrease the fuel cell operating temperature, the thickness of yttria stabilized zirconia thin films is reduced. Often, these thin membranes suffer from mechanical failure and gas permeability. To improve these mechanical issues, a glancing angle deposition approach is used to grow yttria stabilized zirconia thin films with tilted columnar structures. Changes of the material flux direction during the deposition result in a dense, zigzag-like structure with columnar crystallites. This structure reduces the elastic modulus of these membranes as compared to columnar yttria stabilized zirconia thin films as monitored by nano-indentation which makes them more adaptable to applied stress.

Structure and energy calculations of pristine and COOH-modified model single wall carbon nanotubes (SWCNTs) of different length were performed at B3LYP/6-31G* level of theory. From 1 to 9 COOH groups were added at the end of the nanotube. The differences in structure and energetics of partially and fully functionalized SWCNTs at one end of the nanotube are observed. Up to nine COOH groups could be added at one end of (9,0) zigzag SWCNT in case of full functionalization. However, for (5,5) armchair SWCNT, the full functionalization was impossible due to steric crowding and rim deformation. The dependence of substituent attachment energy on the number of substituents at the carbon nanotube rim was observed.

The electronic transport properties of zigzag GaN nanotubes (n, 0) (4 {<=} n {<=} 9) have been calculated using the density functional theory and non-equilibrium Green's functions method. Firstly, the density functional theory (DFT) is used to optimize and calculate the electronic structure of GaNNTs (n, 0) (4{<=}n{<=}9). Secondly, DFT and non-equilibrium Green function (NEGF) method are also used to predict the electronic transport properties of GaNNTs two-probe system. The results showed: there is a corresponding relation between the electronic transport properties and the valley of state density of each GaNNT. In addition, the volt-ampere curve of GaNNT is approximately linear.

In this paper, we investigate the influence of point structural defects on the transport properties of zigzag graphene nanoribbons (ZGNRs) under uniaxial strain field, using the numerical studies based on the ab-initio calculation, the standard tight-binding model and Green's functions. The calculation results show that the direction of applied strain and defect type significantly affect the conductance properties of ZGNRs. The conductance of the defective nanoribbons generally decreases and some dips corresponding to complete electron backscattering is appeared. This behavior is originated from the different coupling between the conducting electronic states influenced by the wave function modification around the Fermi energy which depends on the defect type. We show that the presence of defects leads to a significant increase in local current. Furthermore, we have investigated the strain-tunable spin transport of defective ZGNRs in the presence of the exchange magnetic field and Rashba spin-orbit coupling (RSOC).

In this paper, a zigzag connected autotransformer-based 24-pulse AC-DC converter is designed, modeled and simulated to feed direct torque controlled induction motor drives. Winding arrangements and parameters of the autotransformer and interphase reactor are given. Moreover, the design procedure of the autotransformer is modified to make it suitable for retrofit applications. Simulation results indicate that the system is capable of eliminating up to 21st harmonics in the ac mains current. The effect of load variation and load character is also studied to demonstrate the performance and effectiveness of the proposed 24-pulse converters. A set of power quality indices at ac mains and dc side are presented to compare the performance of 6-, 12- and 24-pulse converters.

Spintronic devices promise new faster and lower energy-consumption electronic systems. Graphene, a versatile material and candidate for next generation electronics, is known to possess interesting spintronic properties. In this paper, by utilizing density functional theory and non-equilibrium green function formalism, we show that Fano resonance can be generated by introducing a break junction in a zigzag graphene nanoribbon (ZGNR). Using this effect, we propose a new spin filtering device that can be used for spin injection. Our theoretical results indicate that the proposed device could achieve high spin filtering efficiency (over 90%) at practical fabrication geometries. Furthermore, our results indicate that the ZGNR break junction lattice configuration can dramatically affect spin filtering efficiency and thus needs to be considered when fabricating real devices. Our device can be fabricated on top of spin transport channel and provides good integration between spin injection and spin transport.

Full Text Available We discuss the thermodynamic stability and magnetic property of zigzag triangular holes (ZTHs in graphene based on the results of first-principles density functional theory calculations. We find that ZTHs with hydrogen-passivated edges in mixed sp2/sp3 configurations (z211 could be readily available at experimental thermodynamic conditions, but ZTHs with 100% sp2 hydrogen-passivation (z1 could be limitedly available at high temperature and ultra-high vacuum conditions. Graphene magnetization near the ZTHs strongly depends on the type and the size of the triangles. While metallic z1 ZTHs exhibit characteristic edge magnetism due to the same-sublattice engineering, semiconducting z211 ZTHs do show characteristic corner magnetism when the size is small <2 nm. Our findings could be useful for experimentally tailoring metal-free carbon magnetism by simply fabricating triangular holes in graphene.

Full Text Available Mainly based on non-equilibrium Green’s function technique in combination with the three-band model, a full atomistic-scale and full quantum method for solving quantum transport problems of a zigzag-edge molybdenum disulfide nanoribbon (zMoSNR structure is proposed here. For transport calculations, the relational expressions of a zMoSNR crystalline solid and its whole device structure are derived in detail and in its integrity. By adopting the complex-band structure method, the boundary treatment of this open boundary system within the non-equilibrium Green’s function framework is so straightforward and quite sophisticated. The transmission function, conductance, and density of states of zMoSNR devices are calculated using the proposed method. The important findings in zMoSNR devices such as conductance quantization, van Hove singularities in the density of states, and contact interaction on channel are presented and explored in detail.

We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Full Text Available Zigzag GaN/Ga2O3 heterogeneous nanowires (NWs were fabricated, and the optical properties and NO gas sensing ability of the NWs were investigated. We find that NWs are most effective at 850 °C at a switching process once every 10 min (on/off = 10 min per each with a mixture flow of NH3 and Ar. The red shift of the optical bandgap (0.66 eV is observed from the UV-vis spectrum as the GaN phase forms. The gas sensing characteristics of the developed sensor are significantly replaced to those of other types of NO sensors reported in literature.

We reveal an edge spin triplet p–wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling. PMID:28186185

The electronic structure of zigzag graphene nanoribbon (ZGNR) is studied using density functional theory. The mechanisms underlying the quantum-confinement effect and edge magnetism in ZGNR are systematically investigated by combining the simulated results and some useful analytic models. The quantum-confinement effect and the inter-edge superexchange interaction can be tuned by varying the ribbon width, and the spin polarization and direct exchange splitting of the edge states can be tuned by varying their electronic occupations. The two edges of ZGNR can be equally or unequally tuned by charge doping or Li adsorption, respectively. The Li adatom has a site-selective adsorption on ZGNR, and it is a nondestructive and memorable approach to effectively modify the edge states in ZGNR. These systematic understanding and effective tuning of ZGNR electronics presented in this work are helpful for further investigation and application of ZGNR and other magnetic graphene systems.

The magnetic properties of zigzag graphene nanoribbon (ZGNR) oxidized by either two single epoxy or one epoxy pair chains were investigated here. The results show that the epoxy pair chain essentially produces finite spin moment for both the antiferromagnetic (AFM) and the ferromagnetic (FM) coupling between the ribbon edges, while the two single epoxy chains oxidized ZGNR and pure ZGNR show the trivial moment for the AFM coupling. The total spin moment has a weak dependence on the position of single epoxy and epoxy pair chains inside the ZGNR and on the width of ZGNR. In addition, the ZGNR oxidized by one epoxy pair chain transitions from a half metal to a semiconductor via tuning the Fermi level when the chain shifts inwards from the ribbon edge. Our results suggest the potential for designing graphene-based spintronics by introducing epoxy pair chains.

The energy spectrum and electronic density of states (DOS) of zigzag graphene nanoribbons with edges reconstructed with topological defects are investigated within the tight-binding method. In case of the Stone–Wales zz(57) edge the low-energy spectrum is markedly changed in comparison to the pristine zz edge. We found that the electronic DOS at the Fermi level is different from zero at any width of graphene nanoribbons. In contrast, for ribbons with heptagons only at one side and pentagons at another one the energy gap at the Fermi level is open and the DOS is equal to zero. The reason is the influence of uncompensated topological charges on the localized edge states, which are topological in nature. This behavior is similar to that found for the structured external electric potentials along the edges.

We have performed density-functional calculations of the transport properties of the zigzag graphene nanoribbon (ZGNR) adsorbed with a single iron atom. Two adsorption configurations are considered, i.e., iron adsorbed on the edge and on the interior of the nanoribbon. The results show that the transport features of the two configurations are similar. However, the transport properties are modified due to the scattering effects induced by coupling of the ZGNR band states to the localized 3d-orbital state of the iron atom. More importantly, one can find that several dips appear in the transmission curve, which is closely related to the above mentioned coupling. We expect that our results will have potential applications in graphene-based spintronic devices.

Edge atomic configuration often plays an important role in dictating the properties of finite-sized two-dimensional (2D) materials. By performing ab initio calculations, we identify a highly stable zigzag edge of phosphorene, which is the most stable one among all the considered edges. Surprisingly, this highly stable edge exhibits a novel nanotube-like structure, which is topologically distinctively different from any previously reported edge reconstruction. We further show that this new edge type can form easily, with an energy barrier of only 0.234 eV. It may be the dominant edge type at room temperature in vacuum condition or even under low hydrogen gas pressure. The calculated band structure reveals that the reconstructed edge possesses a bandgap of 1.23 eV. It is expected that this newly found edge structure may stimulate more studies in uncovering other novel edge types and further exploring their practical applications.

The structure stabilities and electronic properties are investigated by using ab initio self-consistent-field crystal orbital method based on density functional theory for the one-dimensional (1D) double-wall nanotubes made of n-gon SiO{sub 2} nanotubes encapsulated inside zigzag carbon nanotubes. It is found that formation of the combined systems is energetically favorable when the distance between the two constituents is around the Van der Waals scope. The obtained band structures show that all the combined systems are semiconductors with nonzero energy gaps. The frontier energy bands (the highest occupied band and the lowest unoccupied band) of double-wall nanotubes are mainly derived from the corresponding carbon nanotubes. The mobilities of charge carriers are calculated to be within the range of 10{sup 2}–10{sup 4} cm{sup 2} V{sup −1} s{sup −1} for the hybrid double-wall nanotubes. Young’s moduli are also calculated for the combined systems. For the comparison, geometrical and electronic properties of n-gon SiO{sub 2} nanotubes are also calculated and discussed. - Graphical abstract: Structures and band structures of the optimum 1D Double walls nanotubes. The optimized structures are 3-gon SiO2@(15,0), 5-gon SiO2@(17,0), 6-gon SiO2@(18,0) and 7-gon SiO2@(19,0). - Highlights: • The structure and electronic properties of the 1D n-gon SiO{sub 2}@(m,0)s are studied using SCF-CO method. • The encapsulation of 1D n-gon SiO{sub 2} tubes inside zigzag carbon nanotubes can be energetically favorable. • The 1D n-gon SiO{sub 2}@(m,0)s are all semiconductors. • The mobility of charge carriers and Young’s moduli are calculated.

Full Text Available In this work, we have examined how the multi-vacancy defects induced in the horizontal direction change the energetics and the electronic structure of semiconducting Single-Walled Carbon Nanotubes (SWCNTs. The electronic structure of SWCNTs is computed for each deformed configuration by means of real space, Order(N Tight Binding Molecular Dynamic (O(N TBMD simulations. Energy band gap is obtained in real space through the behavior of electronic density of states (eDOS near the Fermi level. Vacancies can effectively change the energetics and hence the electronic structure of SWCNTs. In this study, we choose three different kinds of semiconducting zigzag SWCNTs and determine the band gap modifications. We have selected (12,0, (13,0 and (14,0 zigzag SWCNTs according to n (mod 3 = 0, n (mod 3 = 1 and n (mod 3 = 2 classification. (12,0 SWCNT is metallic in its pristine state. The application of vacancies opens the electronic band gap and it goes up to 0.13 eV for a di-vacancy defected tube. On the other hand (13,0 and (14,0 SWCNTs are semiconductors with energy band gap values of 0.44 eV and 0.55 eV in their pristine state, respectively. Their energy band gap values decrease to 0.07 eV and 0.09 eV when mono-vacancy defects are induced in their horizontal directions. Then the di-vacancy defects open the band gap again. So in both cases, the semiconducting-metallic ¬- semiconducting transitions occur. It is also shown that the band gap modification exhibits irreversible characteristics, which means that band gap values of the nanotubes do not reach their pristine values with increasing number of vacancies.

We present a systematic study of the structural and electronic properties of Cu{sub N}@(n,0) (N=1, 2, 4 for n=6, 7, 8 and N=12, 16 for n=10) combined systems using the first-principle calculations. We find that CuNWs encapsulated inside the (6,0) CNTs prefer to form a single linear chain on the tube axis, while those in (7,0) and (8,0) CNTs tend to form a zigzag chain. The smaller formation energies of −2.265 eV for Cu{sub 12}@(10,0) combined system and −2.271 eV for Cu{sub 16}@(10,0) combined system indicate that these two systems are more stable than the other systems studied here, and more complex configurations of CuNWs are expected encapsulating into broader CNTs. Besides having high stability, the Cu{sub 16}@(10,0) combined system with quantum conductance of 3G{sub 0} is under the protection of the outer (10,0) CNT from oxidation, thus can be expected to have potential applications in building nanodevices. The asymmetry distribution of the down-spin and up-spin channels results in a net magnetic moment of 0.59μB for the Cu{sub 2}@(7,0) combined system. - Highlights: • A linear [zigzag] Cu chain is preferred inside the (6,0) [(7,0) and (8,0)] CNTs. • The highest stability and quantum conductance make Cu{sub 16}@(10,0) a potential application. • Among all Cu{sub N}@(n,0), only Cu{sub 2}@(7,0) has a net magnetic moment of 0.59μB.

The possibility that non-magnetic materials such as carbon could exhibit a novel type of s-p electron magnetism has attracted much attention over the years, not least because such magnetic order is predicted to be stable at high temperatures. It has been demonstrated that atomic-scale structural defects of graphene can host unpaired spins, but it remains unclear under what conditions long-range magnetic order can emerge from such defect-bound magnetic moments. Here we propose that, in contrast to random defect distributions, atomic-scale engineering of graphene edges with specific crystallographic orientation--comprising edge atoms from only one sub-lattice of the bipartite graphene lattice--can give rise to a robust magnetic order. We use a nanofabrication technique based on scanning tunnelling microscopy to define graphene nanoribbons with nanometre precision and well-defined crystallographic edge orientations. Although so-called 'armchair' ribbons display quantum confinement gaps, ribbons with the 'zigzag' edge structure that are narrower than 7 nanometres exhibit an electronic bandgap of about 0.2-0.3 electronvolts, which can be identified as a signature of interaction-induced spin ordering along their edges. Moreover, upon increasing the ribbon width, a semiconductor-to-metal transition is revealed, indicating the switching of the magnetic coupling between opposite ribbon edges from the antiferromagnetic to the ferromagnetic configuration. We found that the magnetic order on graphene edges of controlled zigzag orientation can be stable even at room temperature, raising hopes of graphene-based spintronic devices operating under ambient conditions.

We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search in

The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.

A brief overview is presented of some theoretical work on the symmetry breaking of electronic wavefunctions that followed the early work on Bagus and Schaefer who observed that a considerable lower SCF energy could be obtained for an ionized state of the O2 molecule with a 1s hole if the symmetry re

We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search in

It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.

We show that it is not possible to UV-complete certain low-energy effective theories with spontaneously broken space-time symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform non-linearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of space-time and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.

The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)

The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.

The purpose of this book (I quote verbatim from the back cover) is to 'shed light upon the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory', a very laudable aim. The content divides fairly clearly into four sections (and origins). After a brief introduction, chapters 2-6 review the 'Structure of gravity as a theory based on spacetime gauge symmetries'. This is fairly straightforward material, apparently based on a one-semester graduate course taught at the University of Belgrade for about two decades, and, by implication, this is a reasonably accurate description of its level and assumed knowledge. There follow two chapters of new material entitled 'Gravity in flat spacetime' and 'Nonlinear effects in gravity'. The final three chapters, entitled 'Supersymmetry and supergravity', 'Kaluza-Klein theory' and 'String theory' have been used for the basis of a one-semester graduate course on the unification of fundamental interactions. The boo...

The 1982 summer school on nuclear physics, organized by the Nuclear Physics Division of the Netherlands' Physical Society, was the fifth in a series that started in 1963. The number of students attending has always been about one hundred, coming from about thirty countries. The theme of this year's school was symmetry in nuclear physics. This book covers the material presented by the enthusi­ astic speakers, who were invited to lecture on this subject. We think they have succeeded in presenting us with clear and thorough introductory talks at graduate or higher level. The time schedule of the school and the location allowed the participants to make many informal contacts during many social activities, ranging from billiards to surf board sailing. We hope and expect that the combination of a relaxed atmosphere during part of the time and hard work during most of the time, has furthered the interest in, and understanding of, nuclear physics. The organization of the summer school was made possible by substantia...

We investigate electronic transport properties in symmetric and asymmetric zigzag graphene nanoribbons (ZGNRs) saturated by hydrogen atoms on both edges. The current versus voltage behavior is calculated by the non-equilibrium Green's function method for quantum transport. The ZGNRs transport properties depend on width and structural symmetry. When the spin effects are taken into account, the current-voltage curves change obviously and the spin filter phenomena appear. The result suggests that the ZGNRs might have application potential in constant flow sources and play an important role in future spintronic devices.%通过计算模拟研究了对称和非对称的边缘被氢原子饱和的锯齿型石墨烯纳米带(ZGNRs)的电子输运特性.电流与电压的关系是由量子输运的非平衡格林函数方法计算获得.研究表明,ZGNRs输运性质取决它们的宽度及对称性等因素.如果在计算中考虑自旋效应,我们发现,电流-电压曲线有明显的改变,并与自旋过滤效应存在相关性.结果表明,ZGNRs具有作为恒流源材料的潜在应用价值且可能在未来的自旋电子器件中扮演重要角色.

By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials ...

A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.

Lorentz symmetry is a cornerstone of modern physics. As the spacetime symmetry of special relativity, Lorentz invariance is a basic component of the standard model of particle physics and general relativity, which to date constitute our most successful descriptions of nature. Deviations from exact symmetry would radically change our view of the universe and current experiments allow us to test the validity of this assumption. In this talk, I describe effects of Lorentz violation in cosmic rays and gamma rays that can be studied in current observatories.

We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shift cannot be neglected. We find that anti-symmetric states are subradiant states for distribution with reflection symmetry. These states can be prepared by anti-symmetric optical modes and converted to superradiant states by properly tailored 2\\pipulses. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Z b_L bbar_L coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) x U(1)_X = SU(2)_L x SU(2)_R x P_LR x U(1)_X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)_L x U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M to 0) and standard-model-like (M to infinity) limits.

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zbb coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) x U(1)_X = SU(2)_L x SU(2)_R x P_{LR} x U(1)_X symmetry that protects the Zbb coupling. This symmetry is softly broken to the gauged SU(2)_L x U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M to 0) and standard-model-like (M to infinity) limits.

We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.

We propose a generalization of the isometry transformations to the geometric context of the field theories with spin where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations that leave invariant the equations of the fields with spin have generators with specific spin terms which represent new physical observables. The examples we present are the generators of the central symmetry and those of the maximal symmetries of the de Sitter and anti-de Sitter spacetimes derived in different tetrad gauge fixings. Pacs: 04.20.Cv, 04.62.+v, 11.30.-j

The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.

Dynamical Symmetry Breaking (DSB) is a concept theorists rely on very often in the discussions of strong dynamics, model building, and hierarchy problems. In this talk, I will discuss why this is such a permeating concept among theorists and how they are used in understanding physics. I also briefly review recent progress in using dynamical symmetry breaking to construct models of supersymmetry breaking and fermion masses.

We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples...

Based on both very obvious isospin effect of the neutron-proton number ratio of nucleon emissions (n/p)nucl on symmetry potential and (n/p)nucl's sensitive dependence on symmetry potential in the nuclear reactions induced by halo-neutron projectiles, compared to the same mass stable projectile, probing symmetry potential is investigated within the isospin-dependent quantum molecular dynamics with isospin and momentum-dependent interactions for different symmetry potentials U1sym and U2sym. It is found that the neutron-halo projectile induces very obvious increase of (n/p)nucl and strengthens the dependence of (n/p)nucl on the symmetry potential for all the beam energies and impact parameters, compared to the same mass stable projectile under the same incident channel condition. Therefore (n/p)nucl induced by the neutron-halo projectile is a more favourable probe than the normal neutron-rich and neutron-poor projectiles for extracting the symmetry potential.

We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved $Z_2$ in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the $R$-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example,...

The growth model and electronic properties of the capped zigzag single- and double-walled silicon nanotubes (SWSiNTs and DWSiNTs) are studied with the Density Functional Theory (DFT) method. Particularly, the morphologies of the silicon nanotubes (SiNTs) and the layer-by-layer growth process are explored. Capping of SiNTs is explained well in terms of pentagons. It seems that pentagons or heptagons play apivotal role during the SiNTs growth. Moreover, the structures of the finite SWSiNTs and DWSiNTs are studied. Finally, the infinite SWSiNTs and DWSiNTs can be set up with the repeat unit cells based on the periodic trait of the corresponding finite SiNTs. All of the zigzag SWSiNTs and DWSiNTs have a narrow band gap.

In this paper, the density functional theory calculations are used to obtain the elastic properties of zigzag phosphorene nanotubes. Besides, based on the similarity between phosphorene nanotubes and a space-frame structure, a three-dimensional finite element model is proposed in which the atomic bonds are simulated by beam elements. The results of density functional theory are employed to compute the properties of the beam elements. Finally, using the proposed finite element model, the elastic modulus of the zigzag phosphorene nanotubes is computed. It is shown that phosphorene nanotubes with larger radii have larger Young's modulus. Comparing the results of finite element model with those of density functional theory, it is concluded that the proposed model can predict the elastic modulus of phosphorene nanotubes with a good accuracy.

A microwave quasi-periodic pulsation with zigzag pattern (Z-QPP) in a solar flare on 2005-01-15 is observed by the Chinese Solar Broadband Spectrometer in Huairou (SBRS/Huairou) at 1.10-1.34 GHz. The zigzag pulsation occurred just in the early rising phase of the flare with weakly right-handed circular polarization. Its period is only several decades millisecond. Particularly, before and after the pulsation, there are many spectral fine structures, such as zebra patterns, fibers, and millisecond spikes. The microwave Z-QPP can provide some kinematic information of the source region in the early rising phase of the flare, and the source width changes from ~1000 km to 3300 km, even if we have no imaging observations. The abundant spectral fine structures possibly reflect the dynamic features of non-thermal particles.

The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.

The Kubo formula is used to extract the electrical conductivity (EC) of different diameters of doped zigzag carbon nanotubes and their corresponding unzipped armchair graphene nanoribbons, as a function of temperature and chemical potential, within the tight-binding Hamiltonian model and Green's functions approach. The results reveal more sensitivity to temperature for semiconducting systems in addition to a decrease in EC of all systems with increasing cross-sections.

A new organo-directed titanium phosphate, [NH3CH2CH2NH3]·[TiO(HPO4)2], was synthesized by the solvothermal method and its structure was determined by single crystal X-ray diffraction. The structure consists of 1-D zigzag chains built up from trans-corner-sharing titanium oxo octahedra running along the b axis, with fused Ti2P three-membered rings being attached to the - Ti - O - Ti - O - backbone.

In this work, the tridiagonal method is used to distinguish between edges modes and area modes to study the edge sites properties effect on edge localized states of semi-infinite zigzag 2D honeycomb graphene sheet. The results show a realistic behavior for the dependance of edge localized states of zigzag graphene on the edge sites properties which explaining the experimental results of measured local density of states at the edge of graphene, while at the same time removing the inconsistence...

The structure stabilities and electronic properties are investigated by using ab initio self-consistent-field crystal orbital method based on density functional theory for the one-dimensional (1D) double-wall nanotubes made of n-gon SiO2 nanotubes encapsulated inside zigzag carbon nanotubes. It is found that formation of the combined systems is energetically favorable when the distance between the two constituents is around the Van der Waals scope. The obtained band structures show that all the combined systems are semiconductors with nonzero energy gaps. The frontier energy bands (the highest occupied band and the lowest unoccupied band) of double-wall nanotubes are mainly derived from the corresponding carbon nanotubes. The mobilities of charge carriers are calculated to be within the range of 102-104 cm2 V-1 s-1 for the hybrid double-wall nanotubes. Young's moduli are also calculated for the combined systems. For the comparison, geometrical and electronic properties of n-gon SiO2 nanotubes are also calculated and discussed.

We study numerically the effect of the edge states on the conductance and thermopower in zigzag phosphorene nanoribbons (ZPNRs) based on the tight-binding model and the scattering-matrix method. It is interesting to find that the band dispersion, conductance, and thermopower can be modulated by applying a bias voltage and boundary potentials to the two layers of the ZPNRs. Under a certain bias voltage, the twofold-degenerate quasi-flat-edge bands split perfectly. The conductance can be switched off, and the thermopower around zero energy increases. In addition, when only the boundary potential of the top layer or bottom layer is adjusted, only one edge band bends and merges into the bulk band. The first conductance plateau is strongly decreased to e2/h around zero energy. In particular, when the two boundary potentials are adjusted, all the edge bands bend and fully merge into the bulk band, and the bulk energy gap is maximized. More interestingly, a pronounced conductance plateau with G =0 is found around zero energy, which is attributable to the opening of the bulk energy gap between the valence and conduction bands. Meanwhile, the thermopower can be enhanced more than twice compared to that of the perfect ZPNRs. The large magnitude of thermopower is ascribed to the appearance of the bulk energy gap around zero energy. Our results show that the modulated ZPNRs are more reliable in a thermoelectric application.

Full Text Available This article presents an experimental investigation on the heat transfer performance and pressure drop characteristic of two types of nanofluids flowing through microchannel heat sink with multiple zigzag flow channel structures (MZMCHS. SiO2 nanoparticles dispersed in DI water with concentrations of 0.3 and 0.6 vol.% were used as working fluid. MZMCHS made from copper material with dimension of 28 × 33 mm. Hydraulic diameter of MZMCHs is designed at 1 mm, 7 number of flow channels and heat transfer area is about 1,238 mm2. Effects of particle concentration and flow rate on the thermal and hydraulic performances are determined and then compare with the common base fluid. The results indicated that the heat transfer coefficient of nanofluids was higher than that of the water and increased with increasing particle concentration as well as Reynolds number. For pressure drop, the particle concentrations have no significant effect on the pressure drop across the test section.

The magnetic and electronic properties of hydrogenated and halogenated group-IV zigzag nanoribbons (ZNRs) are investigated by first-principles density functional calculations. Fascinatingly, we find that all the ZNRs have magnetic edges with a rich variety of electronic and magnetic properties tunable by selecting the parent and passivating elements as well as controlling the magnetization direction and external strain. In particular, the electric property of the edge band structure can be tuned from the conducting to insulating with a band gap up to 0.7 eV. The last controllability would allow us to develop magnetic on-off nano-switches. Furthermore, ZNRs such as SiI, Ge, GeI and SnH, have fully spin-polarized metallic edge states and thus are promising materials for spintronics. The calculated magnetocrystalline anisotropy energy can be as large as ~9 meV/edge-site, being 2×103 time greater than that of bulk Ni and Fe (~5 μeV/atom), and thus has great potential for high density magneto-electric data-storage devices. Finally, the calculated exchange coupling strength and thus magnetic transition temperature increases as the applied strain goes from ‑5% to 5%. Our findings thus show that these ZNRs would have exciting applications in next-generation electronic and spintronic nano-devices.

By means of density functional theory computations, we demonstrated that C2H4 is the ideal terminal group for zigzag graphene nanoribbons (zGNRs) in terms of preserving the edge magnetism with experimental feasibility. The C2H4 terminated zGNRs (C2H4-zGNRs) with pure sp(2) coordinated edges can be stabilized at rather mild experimental conditions, and meanwhile reproduce the electronic and magnetic properties of those hydrogen terminated zGNRs. Interestingly, the electronic structures and relative stability of C2H4-zGNRs with different edge configurations can be well interpreted by employing the Clar's rule. The multiple edge hyperconjugation interactions are responsible for the enhanced stability of the sp(2) coordinated edges of C2H4-zGNRs. Moreover, we demonstrated that even pure sp(2) termination is not a guarantee for edge magnetism, for example, C2H2 termination can couple to the π-electron system of zGNRs, and destroy the magnetism. Our studies would pave the way for the application of zGNRs in spintronics.

This paper makes a complete investigation of flexible longitudinal zigzag (FLZ) energy harvesters for the purpose of enhancing energy harvesting from low-frequency and low-amplitude excitation. A general theoretical model of the FLZ energy harvesters with large joint block mass is proposed. In order to verify the accuracy of the theoretical model, both experimental results and finite element analysis via ANSYS software are presented. Results show that the theoretical model can successfully predict the dynamic response and the output power of the FLZ energy harvesters. Both theoretical and experimental results demonstrate that the proposed energy harvesters can effectively harvest vibration energy even when the direction of excitation relative to the harvester varies from 0° to 90°. Under the low excitation level of 0.18 m s‑2, the experimental maximum output power of a FLZ energy harvester with five beams was found to be 1.016 mW. Finally, the results indicate that the proposed structure is capable of effective energy conversion across a large range of excitation angles at low-frequency and low-amplitude excitations, which makes it suitable for a wide range of working conditions.

Full Text Available When new predators invade a habitat, either through range extensions or introductions, prey may be at a high risk because they do not recognize the predators as dangerous. The nine-banded armadillo (Dasypus novemcinctus has recently expanded its range in North America. Armadillos forage by searching soil and leaf litter, consuming invertebrates and small vertebrates, including salamanders. We tested whether Ozark zigzag salamanders (Plethodon angusticlavius from a population coexisting with armadillos for about 30 years exhibit antipredator behavior in the presence of armadillo chemical cues and whether they can discriminate between stimuli from armadillos and a nonpredatory sympatric mammal (white-tailed deer, Odocoileus virginianus. Salamanders appeared to recognize substrate cues from armadillos as a threat because they increased escape behaviors and oxygen consumption. When exposed to airborne cues from armadillos, salamanders also exhibited an antipredator response by spending more time in an inconspicuous posture. Additionally, individually consistent behaviors across treatments for some response variables suggest the potential for a behavioral syndrome in this species.

Realization of half-metallicity in low dimensional materials is a fundamental challenge for nano spintronics, which is a critical component for next-generation information technology. Using the method of generalized Bloch theorem, we show that an in-plane bending can induce inhomogeneous strains, which in turn lead to spin-splitting in zigzag graphene nanoribbons and results in the highly desired half-metallic state. Unlike the previously proposed scheme that requires unrealistically strong external electric fields, the obtained half-metallicity with sizeable half-metallic gap and high energetic stability of magnetic order of edge states requires only relatively low-level strain in the in-plane bending. Given the superior structural flexibility of graphene and the recent experimental advances in controllable synthesis of graphene nanoribbons, our design provides a hitherto most practical approach to the realization of half-metallicity in low dimensional systems. This work, thus paves a way towards the design of nanoscale spintronic devices through strain engineering.

We present a systematic study of the structural and electronic properties of CuN@(n,0) (N=1, 2, 4 for n=6, 7, 8 and N=12, 16 for n=10) combined systems using the first-principle calculations. We find that CuNWs encapsulated inside the (6,0) CNTs prefer to form a single linear chain on the tube axis, while those in (7,0) and (8,0) CNTs tend to form a zigzag chain. The smaller formation energies of -2.265 eV for Cu12@(10,0) combined system and -2.271 eV for Cu16@(10,0) combined system indicate that these two systems are more stable than the other systems studied here, and more complex configurations of CuNWs are expected encapsulating into broader CNTs. Besides having high stability, the Cu16@(10,0) combined system with quantum conductance of 3G0 is under the protection of the outer (10,0) CNT from oxidation, thus can be expected to have potential applications in building nanodevices. The asymmetry distribution of the down-spin and up-spin channels results in a net magnetic moment of 0.59μB for the Cu2@(7,0) combined system.

Half metals are the primary ingredients for the realization of novel spintronic devices. In the present work, by employing density functional theory based first-principles calculation, we predict half metallic behavior in fluorine passivated zigzag graphene nanoribbons (F-ZGNR). Four different structures have been investigated viz. one edge F passivated ZGNR (F-ZGNR-1), both edges F passivated ZGNR (F-ZGNR-2), F passivation on alternate sites in first configuration (alt-1) and F passivation on alternate sites in second configuration (alt-2). Interestingly, it is noticed that F passivation is analogous to H passivation (pristine), however, F-ZGNR are reckoned energetically more stable than pristine ones. An spin induced band gap is noticed for all F-ZGNR irrespective of their widths although its magnitude is slightly less than the pristine counterparts. With an external transverse electric field, ribbons undergo semiconducting to half metallic transformation. The observed half metallic character with enhanced stability present F-ZGNR as a better candidate than pristine ZGNR towards the realization of upcoming spintronic devices.

We theoretically propose a dual-channel current valve based on a three terminal zigzag graphene nanoribbon (ZGNR) junction driven by three asymmetric time-dependent pumping potentials. By means of the Keldysh Green’s function method, we show that two asymmetric charge currents can be pumped in the different left-right terminals of the device at a zero bias, which mainly stems from the single photon-assisted pumping approximation and the valley valve effect in a ZGNR p-n junction. The ON and OFF states of pumped charge currents are crucially dependent on the even-odd chain widths of the three electrodes, the pumping frequency, the lattice potential and the Fermi level. Two-tunneling spin valves are also considered to spatially separate and detect 100% polarized spin currents owing to the combined spin pump effect and the valley selective transport in a three terminal ZGNR ferromagnetic junction. Our investigations might be helpful to control the spatial and spin degrees of freedom of electrons in graphene pumping devices.

Electron paramagnetic resonance (EPR) study of air-physisorbed defective carbon nano-onions evidences in favor of microwave assisted formation of weakly-bound paramagnetic complexes comprising negatively-charged O2- ions and edge carbon atoms carrying pi-electronic spins. These complexes being located on the graphene edges are stable at low temperatures but irreversibly dissociate at temperatures above 50-60 K. These EPR findings are justified by density functional theory (DFT) calculations demonstrating transfer of an electron from the zigzag edge of graphene-like material to oxygen molecule physisorbed on the graphene sheet edge. This charge transfer causes changing the spin state of the adsorbed oxygen molecule from S = 1 to S = 1/2 one. DFT calculations show significant changes of adsorption energy of oxygen molecule and robustness of the charge transfer to variations of the graphene-like substrate morphology (flat and corrugated mono- and bi-layered graphene) as well as edges passivation. The presence of...

This talk presents a kinetic Monte Carlo study of the relaxation dynamics of [110] steps on a vicinal (001) simple cubic surface. This system is interesting because [110] steps have different elementary excitation energetics and favor step diffusion more than close-packed [100] steps. In this talk we show how this leads to relaxation dynamics showing greater fluctuations on a shorter time scale for [110] steps as well as 2-bond breaking processes being rate determining in contrast to 3-bond breaking processes for [100] steps. The existence of a steady state is shown via the convergence of terrace width distributions at times much longer than the relaxation time. In this time regime excellent fits to the modified generalized Wigner distribution (as well as to the Berry-Robnik model when steps can overlap) were obtained. Also, step-position correlation function data show diffusion-limited increase for small distances along the step as well as greater average step displacement for zigzag steps compared to straight steps for somewhat longer distances along the step. Work supported by NSF-MRSEC Grant DMR 05-20471 as well as a DOE-CMCSN Grant.

The effects of electron-electron and spin-orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analysed theoretically. The thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin-orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions also has a significant impact on the transport and thermoelectric characteristics of the nanoribbons. The spin-orbit interaction also determines the in-plane magnetic easy axis. The thermoelectric properties of nanoribbons with in-plane magnetic moments are compared to those of nanoribbons with edge magnetic moments oriented perpendicularly to their plane. Nanoribbons with ferromagnetic alignment of the edge moments are shown to reveal spin thermoelectricity in addition to the conventional one.

Quantum transport and spin current in a zigzag SiC nanoribbon device under a thermal gradient are investigated theoretically within the framework of the Landauer-Büttiker formalism using a first-principles technique. It is found that the edge state transport channels can be turned off or kept open by specific edge doping, and different spin channels can be controlled separately. Interestingly, by replacing an edge C atom with a B atom and an edge Si atom with a P atom in the scattering region, a Seebeck thermopower with different signs for different spins and a finite conductance for both spins can be obtained in the linear response regime. The subsequent thermoelectric field drives electrons of different spin channels in opposite directions, which leads unambiguously to a spin current. More importantly, by tuning the chemical potential and working temperature, pure spin current can be achieved. This provides a promising two-dimensional candidate system for producing pure spin current via the spin-dependent Seebeck effect.

Using non-equilibrium Green's function, we study the spin-dependent electron transport properties in a zigzag silicene nanoribbon. To produce and control spin polarization, it is assumed that two ferromagnetic strips are deposited on the both edges of the silicene nanoribbon and an electric field is perpendicularly applied to the nanoribbon plane. The spin polarization is studied for both parallel and anti-parallel configurations of exchange magnetic fields induced by the ferromagnetic strips. We find that complete spin polarization can take place in the presence of perpendicular electric field for anti-parallel configuration and the nanoribbon can work as a perfect spin filter. The spin direction of transmitted electrons can be easily changed from up to down and vice versa by reversing the electric field direction. For parallel configuration, perfect spin filtering can occur even in the absence of electric field. In this case, the spin direction can be changed by changing the electron energy. Finally, we investigate the effects of nonmagnetic Anderson disorder on spin dependent conductance and find that the perfect spin filtering properties of nanoribbon are destroyed by strong disorder, but the nanoribbon retains these properties in the presence of weak disorder.

A matrix formalism is used to derive the analytical Green's functions describing correlations between any two atomic sites on a zigzag (ZZ) graphene nanoribbon, incorporating modified electronic hopping values between edge sites that may be distinct from the hopping between interior sites. An analysis of the poles of our Green's functions shows two distinct types of localized edge modes in the electronic spectrum. The first of these, the "zero" mode, is a topologically induced mode arising from the bipartite honeycomb lattice structure of graphene and is always present along ZZ edges. The second type of localized edge mode is present at edges when the edge-to-bulk hopping ratio deviates significantly from unity. The correlations between edge sites are found to exhibit strikingly different features when mediated by the zero edge mode compared with mediation by the "modified" edge mode. In particular, the zero-mode spectral intensity for correlations between two atomic sites along opposite edges can be comparable in strength with that between two sites on the same edge of a finite-width ribbon, before it eventually tends to zero as the ribbon width tends to infinity. This remarkable behavior shows a strong dependence on the sublattice labels of the sites and is in contrast with properties of the modified hopping edge modes. The explicit form of our analytical expressions for the electronic spectrum enables us to predict the zero-mode properties (including frequency, spatial attenuation, and intensity) when the hopping values along ZZ edges are modified.

The capability to print three-dimensional (3D) cellular tubes is not only a logical first step towards successful organ printing but also a critical indicator of the feasibility of the envisioned organ printing technology. A platform-assisted 3D inkjet bioprinting system has been proposed to fabricate 3D complex constructs such as zigzag tubes. Fibroblast (3T3 cell)-based tubes with an overhang structure have been successfully fabricated using the proposed bioprinting system. The post-printing 3T3 cell viability of printed cellular tubes has been found above 82% (or 93% with the control effect considered) even after a 72-h incubation period using the identified printing conditions for good droplet formation, indicating the promising application of the proposed bioprinting system. Particularly, it is proved that the tubular overhang structure can be scaffold-free fabricated using inkjetting, and the maximum achievable height depends on the inclination angle of the overhang structure. As a proof-of-concept study, the resulting fabrication knowledge helps print tissue-engineered blood vessels with complex geometry.

We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the noninteracting limit, the Kane-Mele (KM) model is known to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective interedge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb (Hubbard) interaction and the interedge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase, and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the interedge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases. The relevance of our results for graphene is discussed.

First-principles study based on density functional theory has been employed to investigate width-dependent structural stability and magnetic properties of monolayer zigzag MoS2 nanoribbons (ZZ-MoS2 NRs). The width N = 4-6 (the numbers of zigzag Mo-S chains along the ribbon length) are considered. The results show that all studied ZZ-MoS2 NRs are less stable than two-dimensional MoS2 monolayer, exhibiting that a broader width ribbon behaves better structural stability and an inversely proportional relationship between the structural stability (or the ribbon with) and boundary S-Mo interaction. Electronic states imply that all ZZ-MoS2 NRs exhibit magnetic properties, regardless of their widths. Total magnetic moment increases with the increasing width N, which is mainly ascribed to the decreasing S-Mo interaction of the two zigzag edges. In order to confirm this reason, a uniaxial tension strain is applied to ZZ-MoS2 NRs. It has been found that, with the increasing tension strain, the bond length of boundary S-Mo increases, at the same time, the magnetic moment increases also. Our results suggest the rational applications of ZZ-MoS2 NRs in nanoelectronics and spintronics.

A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.

Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints.

A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries.Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetryCovers both point-group and space-group symmetriesIncludes tutorial solutions

We perform a comprehensive study of the $\\Delta (96)$ family symmetry combined with the generalised CP symmetry $H_{\\rm{CP}}$. We investigate the lepton mixing parameters which can be obtained from the original symmetry $\\Delta (96)\\rtimes H_{\\rm{CP}}$ breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely $G_{\

We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4-6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: firs...

We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.

We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of out model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.

The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University

Two new experiments have detected charge-symmetry breaking, the mechanism responsible for protons and neutrons having different masses. Symmetry is a crucial concept in the theories that describe the subatomic world because it has an intimate connection with the laws of conservation. The theory of the strong interaction between quarks - quantum chromodynamics - is approximately invariant under what is called charge symmetry. In other words, if we swap an up quark for a down quark, then the strong interaction will look almost the same. This symmetry is related to the concept of sup i sospin sup , and is not the same as charge conjugation (in which a particle is replaced by its antiparticle). Charge symmetry is broken by the competition between two different effects. The first is the small difference in mass between up and down quarks, which is about 200 times less than the mass of the proton. The second is their different electric charges. The up quark has a charge of +2/3 in units of the proton charge, while ...

The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .

We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.

Full Text Available Usually, Symmetry and Asymmetry are considered as two opposite sides of a coin: an object is either totally symmetric, or totally asymmetric, relative to pattern objects. Intermediate situations of partial symmetry or partial asymmetry are not considered. But this dichotomy on the classification lacks of a necessary and realistic gradation. For this reason, it is convenient to introduce "shade regions", modulating the degree of Symmetry (a fuzzy concept. Here, we will analyze the Asymmetry problem by successive attempts of description and by the introduction of the Asymmetry Level Function, as a new Normal Fuzzy Measure. Our results (both Theorems and Corollaries suppose to be some new and original contributions to such very active and interesting field of research. Previously, we proceed to the analysis of the state of art.

After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov copies. A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between \\tau and the gauge parameter \\omega defined by \\tau (x) = f( A_{\\mu}^{\\omega}(x)) is ``globally single valued'', where f( A_{\\mu}^{\\omega}(x)) = 0 specifies the gauge condition. As an example of the theory which satisfies this criterion, we comment on a soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren. We also comment on a possible connection of the dynamical instability of BRST symmetry with the Gribov problem on the basis of an index notion.

Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.

Full Text Available We study the emergence of Heisenberg (Bianchi II algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N=2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U(1×U(1 at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg⋉U(1. We finally discuss the realization of the latter by gauging appropriate Sp(2,4 generators in N=2 conformal supergravity.

These are intended to be introductory notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some elementary background material and proceed to our discussion by examining several interesting problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of `symmetry surfing', i.e., by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.

Full Text Available The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review.

This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.

The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigorous in the sense that their correctness is limited only to the correct choice of symmetry of the internal dynamics. The book is basically intended for scientists working in the field of molecular spectroscopy, quantum and structural chemistry.

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the {{mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the Z_5 symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.

This is a survey covering aspects of varied work of the authors with Mohammed Abouzaid, Paul Hacking, and Sean Keel. While theta functions are traditionally canonical sections of ample line bundles on abelian varieties, we motivate, using mirror symmetry, the idea that theta functions exist in much greater generality. This suggestion originates with the work of the late Andrei Tyurin. We outline how to construct theta functions on the degenerations of varieties constructed in previous work of the authors, and then explain applications of this construction to homological mirror symmetry and constructions of broad classes of mirror varieties.

The wide band gap of boron nitride (BN) materials has been a major bottleneck for a wider application of BN in electronics. In this work, density functional theory computations were used to study the band structure of zigzag BN nanoribbons (BNNRs). Due to the ionic origin of the BN band gap, a heterogeneous edge decoration is an effective way to modulate the electronic band structure of BNNRs. This study demonstrates that a metallic behavior and magnetism can be realized by applying a NO{sub 2}–NH{sub 2} pair edge decoration. Although the lone electron pair of the NH{sub 2} group is partly responsible for the metallic behavior, the effective potential difference induced by the donor–acceptor pair is also crucial for metallic behavior. Furthermore, these newly formed BNNRs were found to be more stable than H-passivated BNNRs. This simple chemical modification method offers great opportunities for the development of future BNNR-based electronic devices. - Graphical abstract: Due to the ionic origin of a BN band gap, heterogeneous edge decoration is an effective way to modulate its electronic structures. Metallicity and magnetism can be realized by NO{sub 2}–NH{sub 2} pair decoration. Although the N lone pair electrons in NH{sub 2} group are responsible for the metallicity, the effective potential difference induced by a donor–acceptor pair is crucial for the formation of metallicity. - Highlights: • Heterogeneous edge decoration is effective for tuning BNNRs' electronic structures. • NO{sub 2}–NH{sub 2} pair decoration can lead to metallic behavior and magnetism for BNNRs. • The effective potential difference is crucial for the formation of metallicity. • NO{sub 2}–NH{sub 2} pair decorated BNNRs is more stable than H-passivated ones.

This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.

We discuss the (non)-restoration of global and local symmetries at high temperature. First, we analyze a two-scalar model with $Z_2 \\times Z_2$ symmetry using the exact renormalization group. We conclude that inverse symmetry breaking is possible in this kind of models within the perturbative regime. Regarding local symmetries, we consider the $SU(2) \\otimes U(1)$ gauge symmetry and focus on the case of a strongly interacting scalar sector. Employing a model-independent chiral Lagrangian we find indications of symmetry restoration.

Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry.

Partial dynamical symmetries (PDS) are shown to be relevant to the interpretation of the $K=0_2$ band and to the occurrence of F-spin multiplets of ground and scissors bands in deformed nuclei. Hamiltonians with bosonic and fermionic PDS are presented.

We propose an order parameter for the symmetry-protected topological (SPT) phases which are protected by Abelian on-site symmetries. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B , two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A , B , and the boundaries of the system. In the case of one-dimensional systems we prove that in the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the nontrivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Also, we show that there is an intriguing connection between SPT entanglement and the Fourier transform of the string order parameters, which are the traditional tool for detecting SPT phases. This leads to an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters. Finally, we discuss implications of our results in the context of measurement-based quantum computation.

We study chiral symmetry structure at ﬁnite density and temperature in the presence of external magnetic ﬁeld and gravity, a situation relevant in the early Universe and in the core of compact stars. We then investigate the dynamical evolution of phase transition in the expanding early Universe and possible formation of quark nuggets and their survival.

The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait.

The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.

We construct (hybrid) baryons in the flux-tube model of Isgur and Paton. In the limit of adiabatic quark motion, we build proper eigenstates of orbital angular momentum and construct the flavour, spin and J^P of hybrid baryons from the symmetries of the system. The lowest mass hybrid baryon is estimated at approximately 2 GeV.

Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.

Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H= SU(2)_L x SU(2)_R/SU(2)_V with additional symmetry, the nonlinearly realized scale symmetry. Then the SM does have a dynamical gauge boson of the SU(2)_V HLS, "SM rho meson", in addition to the Higgs as a pseudo dilaton as well as the NG bosons to be absorbed into the W and Z. Based on the recent work done with S. Matsuzaki and H. Ohki, I discuss a novel possibility that the SM rho meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call "Dark SM skyrmi...

Our current knowledge of particle physics is described by the Standard Model (SM). This model, however, leaves important observations unexplained. To answer these outstanding questions, as of yet, unknown physics is required. In the search for new physics, symmetries and their breaking play a guidin

Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L × SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, "SM ρ meson", in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call "dark SM skyrmion (DSMS)".

Full Text Available Graph theory provides an elegant and natural representation of molecular symmetry and the resulting group expressed in terms of permutations is isomorphic to the permutation-inversion group of Longuet-Higgins. In this paper, using the group theory package GAP, the character table and the automorphism group of the Euclidean graph of tetrahydroxycalix[4]arenes were computed.

To evaluate visual outcomes and astigmatism in patients who underwent penetrating keratoplasty (PK) with 2 different incision techniques. Retrospective comparison of a consecutive surgical series. Fifty-seven consecutive patients who underwent PK at the University of California, Irvine, academic referral practice. A comparison of 49 eyes of 43 patients that underwent femtosecond laser zig-zag incision pattern PK versus 17 eyes of 14 patients that underwent conventional Barron suction trephination PK performed contemporaneously. All PKs were closed with an identical, 24-bite running nylon suture technique. Topographically determined astigmatism, best spectacle-corrected visual acuity (BSCVA), and recovery of full visual potential. The postoperative follow-up ranged from 1 to 12 months. There was a significant difference in average astigmatism between the groups at postoperative month 1 (P = 0.013) and 3 (P = 0.018). By month 3, the average astigmatism was 3 diopters (D) in the zig-zag group and 4.46 D in the conventional group. Of the patients with normal macular and optic nerve function (n(ZZ) = 32; n(con) = 14), a significant difference in BSCVA was seen at month 1 (P = 0.0003) and month 3 (P = 0.006) with 81% of the zig-zag group versus 45% of the conventional group achieving BSCVA of > or =20/40 by month 3 (P = 0.03). The femtosecond laser generated zig-zag-shaped incision results in a more rapid recovery of BSCVA and induces less astigmatism compared with conventional blade trephination PK. Proprietary commercial disclosure may be found after the references.

Highlights: • We propose Fanning factor and Nusselt number correlations for the airfoil PCHE. • We evaluate the thermal–hydraulic performance for each PCHE type in terms of the total cost. • The zigzag PCHE is the most appropriate IHX for the HTGRs, operating in laminar region. • The straight PCHE is the best for the IHX in the SFRs, operating in turbulent region. - Abstract: A promising candidate for the intermediate heat exchanger (IHX) in high temperature gas-cooled reactors (HTGRs) and sodium-cooled fast reactors (SFRs) is a printed circuit heat exchanger (PCHE) due to its high effectiveness and compactness. We developed the thermal–hydraulic correlations for an airfoil PCHE by three-dimensional computational fluid dynamics (3D-CFD) analysis, which are applicable over the range of Reynolds number from 0 to 150,000, including helium in laminar region and CO{sub 2} in turbulent region. Proposed Fanning factor correlation for the entire range showed the normalized root mean square deviation (NRMSD) as 2.52%. NRMSDs for two Nusselt number models for each flow region were calculated as 4.66% and 0.82%. We compared the total cost considering material and operation cost for the IHXs in HTGRs and SFRs with 4 types of PCHEs, which are straight, zigzag, S-shape, and airfoil PCHEs. For the IHXs of pebble bed modular reactor (PBMR) operating in the laminar region, the zigzag PCHE is the best option because of its lowest pressure drop and relatively high heat transfer area. The straight PCHE for the IHXs of Kalimer-600 is definitely the best option due to its much lower pressure drop, which is one reactor type of the SFRs operating in the turbulent region.

In order to improve the detection accuracy and range of new generation of Forward Looking Infra-Red (FLIR) system for distant targets, its optical system, which usually consists of a fore afocal telescope and rear imaging lenses, is required to has wide spectral range, large entrance pupil aperture, and wide field of view (FOV). In this paper, a new afocal Three-Mirror Anastigmat (TMA) with widened field of view and high demagnification is suggested. Its mechanical structure remains coaxial, but it has zigzag optical axis through properly and slightly decentering and tilting of the three mirrors to avoid its secondary obscuration due to the third mirror as FOV increase. Compared with conventional off-axis TMA, the suggested zigzag-axis TMA is compact, easy-alignment and low-cost. The design method and optimum result of the suggested afocal TMA is presented. Its initial structural parameters are determined with its first-order relationship and primary aberration theory. Slight and proper decentration and tilt of each mirror is leaded in optimization so that its coaxial mechanical structure is held but attainable FOV and demagnification are respectively as wide and as high as possible. As an example, a 5.5-demagnification zigzag-axis afocal TMA with a wavelength range, an entrance pupil diameter, and FOV respectively from 3μm to 12μm, of 320mm, and 2×3.2 degrees and with a real exit pupil, is designed. Its imaging quality is diffraction limited. It is suitable for fore afocal telescope of the so-called third generation FLIR.

Electronic band gaps for optically allowed transitions are calculated for a series of semiconducting single-walled zig-zag carbon nanotubes of increasing diameter within the many-body perturbation theory GW method. The dependence of the evaluated gaps with respect to tube diameters is then compared with those found from previous experimental data for optical gaps combined with theoretical estimations of exciton binding energies. We find that our GW gaps confirm the behavior inferred from experiment. The relationship between the electronic gap and the diameter extrapolated from the GW values is also in excellent agreement with a direct measurement recently performed through scanning tunneling spectroscopy.

A new hybrid piezoelectric composite (HPZC) reinforced with zigzag single-walled carbon nanotubes (CNTs) and piezoelectric fibers is proposed. The novel constructional feature of this composite is that the uniformly aligned CNTs are radially grown on the surface of piezoelectric fibers. A micromechanics model is derived to estimate the effective piezoelectric and elastic properties. It is found that the effective piezoelectric coefficient e31 of the proposed HPZC, which accounts for the in-plane actuation, is significantly higher than that of the existing 1-3 piezoelectric composite without reinforcement with carbon nanotubes and the previously reported hybrid piezoelectric composite (Ray and Batra 2009 ASME J. Appl. Mech. 76 034503).

Quantum transport properties of some Ni-based dinuclear complexes with different polydentate organic ligands have been studied by applying abinitio density functional theory along with nonequilibrium Green's function formulations. It is demonstrated that these materials are capable of showing multifunctional spin dependent properties by the influence of edge states of zigzag edged graphene nanoribbons. The current-voltage characteristics of these materials show spin dependent negative differential resistance behavior, spin filtering effect, and also voltage rectifying property. Proper tuning of these materials can alter these effects which may be utilized in various spintronic devices.

The transformation of titanium phosphate from 1-D chiral- chain(JTP-A) to 2-D layer(TP-J1) has been carefully investigated. Through a hydrolysis-condensation self-assembly pathway, the crystals of TP-J1 can be obtained from the JTP-A phase under hydrothermal conditions. An intermediate material with zigzag chain during the transformation was observed by XRD characterization. A hypothesis of the transformation mechanism is also described in this article. It is noteworthy that ethylenediamine plays an important role in the transformation.

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.

The spatial current distribution in H-terminated zigzag graphene nanoribbons (ZGNRs) under electrical bias is investigated using time-dependent density-functional theory solved on a real-space grid. A projected complex absorbing potential is used to minimize the effect of reflection at simulation cell boundary. The calculations show that the current flows mainly along the edge atoms in the hydrogen terminated pristine ZGNRs. When a vacancy is introduced to the ZGNRs, loop currents emerge at the ribbon edge due to electrons hopping between carbon atoms of the same sublattice. The loop currents hinder the flow of the edge current, explaining the poor electric conductance observed in recent experiments.

We analyse the arguments used in the relativistic context to base the quasi-degeneracy of pseudospin doublets (PSDs) observed in atomic nuclei on the smallness of the single-particle central potential ({sigma}{sub S}+{sigma}{sub 0}), discussing, especially, the implications of the results obtained in the limit {sigma}{sub S}+{sigma}{sub 0}=0. We study also the transition from a relativistic model, where {sigma}{sub S}+{sigma}{sub 0} is a harmonic-oscillator potential and exhibits degenerate PSDs, to a more realistic one with broken pseudospin symmetry. We examine, in particular, the effect of the corresponding pseudospin symmetry-breaking term on the Dirac spinors of the PSDs. An extension of the Nilsson model to the relativistic case is also considered. (orig.)

It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.

We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by envoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with a cosmological constant and a massless scalar carries conformal symmetry. They further claim that such a theory carries another hidden symmetry; a global SO(1,1) symmetry. By deforming around the global SO(1,1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend ...

In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether Gauge Symmetries (NGS). Motivated by this mathematical tool, in this article, we discuss the generalized Noether symmetry of Quintom model of dark energy, which is a two component fluid model of quintessence and phantom fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potentia...

By using first principle calculations we have studied the magnetic, electronic and transport properties of zigzag-graphene nanoribbon (zGNR) with a topological line defect (LD) composed of pentagons and heptagons (5-7). We show that one can engineer the magnetic and electronic properties of the edge passivated zGNR with 5-7 LD through the variation of either the width of the zGNR or the position of the LD. Thus, one can have ferromagnetic behaviour in zGNR by introducing 5-7 LD close to one edge of the ribbon. One can tune the zGNR with 5-7 LD from semi-metallic to semi-metallic semiconductor either by increasing the width of the ribbon or by changing the position of the LD. We have also studied the effect of the doping on the degeneracy of the spin states of 4-4-LD-zGNR. The calculation of transport properties of N-doped 4-4-LD-zGNR reveals that it has high spin filtering efficiencies. The tuning of the spin polarization through the formation of 5-7 LD in zGNR holds a promise for its application in spintronic devices. - Highlights: • The magnetic and electronic properties of zGNR with 5-7 LD can be engineered through the variation of the width of zGNR and the position of LD. • Ferromagnetic behaviour in zGNR can be found by introducing 5-7 LD close to one edge of the ribbon. • Semi-metallic to semi-metallic semiconductor transition occurs by increasing the width of the ribbon or by changing the position of the LD. • There is significant effect of the doping on the degeneracy of the spin states of 4-4-LD-zGNR. • The transport properties calculation of N-doped 4-4-LD-zGNR reveals that it has high spin filtering efficiencies.

We investigate the maximal approximate flavor symmetry in the framework of generic minimal supersymmetric standard model. We consider the low energy effective theory of the flavor physics with all the possible operators included. Spontaneous flavor symmetry breaking leads to the approximate flavor symmetry in Yukawa sector and the supersymmetry breaking sector. Fermion mass and mixing hierachies are the results of the hierachy of the flavor symmetry breaking. It is found that in this theory i...

A group-theoretical connection between horizontal symmetry $\\G$ and fermion mixing is established, and applied to neutrino mixing. The group-theoretical approach is consistent with a dynamical theory based on $U(1)\\times \\G$, but the dynamical theory can be used to pick out the most stable mixing that purely group-theoretical considerations cannot. A symmetry common to leptons and quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the preferred symmetry for leptons.

Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.

We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization symmetry groups which can appear in the three-Higgs-doublet models.

We introduce the notion of a generalized partial dynamical symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in $^{162}$Dy.

We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.

We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial SU(3) symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei. {copyright} {ital 1996 The American Physical Society.}

We discuss the notion of partial dynamical symmetry in relation to nuclear spectroscopy. Explicit forms of Hamiltonians with partial SU(3) symmetry are presented in the framework of the interacting boson model of nuclei. An analysis of the resulting spectrum and electromagnetic transitions demonstrates the relevance of such partial symmetry to the spectroscopy of axially deformed nuclei.

We show that distinct emergent symmetries, such as partial dynamical symmetry and quasi dynamical symmetry, can occur simultaneously in the same or different eigenstates of the Hamiltonian. Implications for nuclear spectroscopy in the rare-earth region and for first-order quantum phase transitions between spherical and deformed shapes, are considered.

In this paper we will discuss Faddeev-Popov method for gauge theories with a general form of gauge symmetry in an abstract way.We will then develope a general formalism for dealing with the BRST symmetry.This formalism will make it possible to analyse the BRST symmetry for any theory.

We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.

We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

The dissipative Hofstadter model, which describes a particle in 2-D subject to a periodic potential, uniform magnetic field, and dissipation, is also related to open string boundary states. This model exhibits an SL(2,Z) duality symmetry and hidden reparametrization invariance symmetries. These symmetries are useful for finding exact solutions for correlation functions.

An analytical treatment of electrostatic and magnetostatic field symmetry, as a function of charge and current distribution symmetry, is proposed. The Newmann Principle, related to the cause-effect symmetry relation, is presented and applied to the characterization of simple configurations. (Author) 5 refs.

Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry $G_f$ to different residual symmetries $G_{\\ell}$ and $G_\

Humans are very sensitive to symmetry in visual patterns. Reaction time experiments show that symmetry is detected and recognized very rapidly. This suggests that symmetry is a highly salient feature. Existing computational models of saliency, however, have mainly focused on contrast as a measure of

Developments during the last eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in Nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.

We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.

Critical Point Symmetries (CPS) appear in regions of the nuclear chart where a rapid change from one symmetry to another is observed. The first CPSs, introduced by F. Iachello, were E(5), which corresponds to the transition from vibrational [U(5)] to gamma-unstable [O(6)] behaviour, and X(5), which represents the change from vibrational [U(5)] to prolate axially deformed [SU(3)] shapes. These CPSs have been obtained as special solutions of the Bohr collective Hamiltonian. More recent special solutions of the same Hamiltonian, to be described here, include Z(5) and Z(4), which correspond to maximally triaxial shapes (the latter with ``frozen'' gamma=30 degrees), as well as X(3), which corresponds to prolate shapes with ``frozen'' gamma=0. CPSs have the advantage of providing predictions which are parameter free (up to overall scale factors) and compare well to experiment. However, their mathematical structure [with the exception of E(5)] needs to be clarified.

We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity-dispersion (GVD) in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity ($\\mathcal{CP}$) symmetry, while the addition of the intra-core cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.

We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity (CSS) models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincare supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coup...

We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.

We present a model of flavor based on a discrete local symmetry that reproduces all fermion masses and mixing angles both in the quark and lepton sectors. The particle content of the model is that of the standard model plus an additional flavon field. All the fields propagate in a fifth universal extra dimension and the flavor scale is associated with the cutoff of the 5D theory which is $\\sim 10$ TeV. The Yukawa matrices as well as the Majorana mass matrix for the neutrinos are generated by higher dimension operators involving the flavon field. When the flavon field acquires a vacuum expectation value it breaks the flavor symmetry and thus generates the Yukawa couplings. The model is consistent with the nearly bimaximal solution to the solar and atmospheric neutrino deficits.

We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow one to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in grand unified theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture. (orig.)

We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in Grand Unified Theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture.

General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.

The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4, and A5. We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S4 model and reproduces the allowed values of the mixing angles, we predict δ=(90°-120°).

The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetr...

Two accounts of quantum symmetry breaking (SSB) in the algebraic approach are compared: the representational and the decompositional account. The latter account is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account: the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.

By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.

This chapter present models of electroweak symmetry breaking arising from strongly interacting sectors, including both Higgsless models and mechanisms involving a composite Higgs. These scenarios have also been investigated in the framework of five-dimensional warped models that, according to the AdS/CFT correspondence, have a four-dimensional holographic interpretation in terms of strongly coupled field theories. We explore the implications of these models at the LHC.

We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group Delta(27). Neutrinos are Dirac fermions and their masses arise in the same way as that of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass

The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalised, including to continuous cases an...

The use of a zig-zag surface coil with a three-pulse Fourier Series Window (FSW) has been suggested as a means by which in vivo NMR spectroscopic studies of human skin can be performed. Using direct numerical simulations of the magnetic field profile of a 10 limb zig-zag surface coil, the role of the FSW in reducing NMR signals originating from the deeper skeletal muscle layers is examined theoretically. The extent of muscle signal contamination is determined for different coil inter-limb spacings and pulse width settings. The optimum inter-limb spacing for studying living human skin, that which minimizes signal contamination and maximizes skin signal collected, is shown to be between 4 and 6 mm. These calculations demonstrate that the FSW and zig-zag surface coil offer a protocol for investigating the metabolism of large areas of surface tissue while keeping signal contamination from the deeper skeletal muscle layers down to an acceptable level.

Full Text Available In this paper THD (Total Harmonic Distortion is analysed and compared by using UPFC in a multi-line transmission system of 500 KV having 5-buses in two different arrangements. The UPFC converters are arranged as a Diode Clamped multilevel Converter (DCMLC that leads to the cost reduction as compared with other multi-level converters. The comparison has been done by both series zig-zag/2Y-2Δ and series zig-zag/4Y transformer configuration for 48-pulses GTO based diode clamped converter. The THD is reduced to 42.59% and 58.82% of input waveform at bus B_2 by using series zig-zag/4Y transformer configuration. This transformer converter configuration also reduces the difficulty of designing the transformer winding ratio. For calculation of THD, FFT analysis is carried out using MATLAB.

The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.

General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.

Full Text Available Latent heat thermal energy storage (TES plays an important role in the advocation of TES in contrast to sensible energy storage because of the large storage energy densities per unit mass/volume possible at a nearly constant thermal energy. In the current study, a heat exchange device with a zigzag configuration containing multiple phase-change-materials (m-PCMs was considered, and an experimental system was built to validate the model for a single PCM. A two-dimensional numerical model was developed using the ANSYS Fluent 14.0 software program. The energy fractions method was put forward to calculate the average Ste number and the influence of Re and Ste numbers on the discharge process were studied. The influence of phase change temperature among m-PCMs on the solidification process has also been studied. A new boundary condition was defined to determine the combined effect of the Re and Ste numbers on the discharging process. The modelling results show that for a given input power, the Ste (or Re number has a significant impact on the discharging process; however, the period value of inlet velocity has almost no impact on it. Besides, the zigzag plate with m-PCMs has a good impact on the temperature shock as “filter action” in the discharging process.

Comparative study has been performed with various channel cross-sectional shapes and channel configurations of a zigzag printed circuit heat exchanger (PCHE), which has been considered as a heat exchanging device for the gas turbine based generation systems. Three-dimensional Reynolds-averaged Navier-Stokes equations and heat transfer equations are solved to analyze conjugate heat transfer in the zigzag channels. The shear stress transport model with a low Reynolds number wall treatment is used as a turbulence closure. The global Nusselt number, Colburn j-factor, effectiveness, and friction factor are used to estimate the thermal-hydraulic performance of the PCHE. Four different shapes of channel cross section (semicircular, rectangular, trapezoidal, and circular) and four different channel configurations are tested to determine their effects on thermal-hydraulic performance. The rectangular channel shows the best thermal performance but the worst hydraulic performance, while the circular channel shows the worst thermal performance. The Colburn j-factor and friction factor are found to be inversely proportional to the Reynolds number in cold channels, while the effectiveness and global Nusselt number are proportional to the Reynolds number.

The spin transport properties of zigzag graphene nanoribbon (ZGNR) hetero-junctions, in which ZGNR electrodes are doped with B or N atoms, are investigated based on spin-polarized density functional theory and non-equilibrium Green's function. ZGNRs are C–H2 bonded at one edge and C–H bonded at the other edge to form asymmetric edge hydrogenation. The spin-polarized currents of ZGNR-based nano-devices with an odd or even number of the zigzag-shaped chains show a perfect bipolar spin-filtering effect on parallel and anti-parallel magnetic configurations. This study provides insights into the design of high-performance graphene-based spin filters. - Highlights: • We have investigated the spin-dependent transport properties of the H2–5(6)ZGNR–H devices with B/N doping in both ZGNR electrodes. • A perfect bipolar spin-filtering effect can be obtained in 5(6)ZGNR-based hetero-structures with P and AP magnetic configurations. • The graphene-based diode can be attained by manipulating the doping positions of B or N atoms in both electrodes.

Localized magnetic impurity centres in graphene can interact through the π-electrons, leading to an effective Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. A RKKY-type study is presented for graphene ribbons with zigzag edges. Specifically investigations of how the edges modify the interaction between two localized magnetic moments are made by using a tight-binding Hamiltonian to describe the hopping of the π-electrons between adjacent sites and a contact term for interactions with the localized moments. In terms of a Green's function formalism for the excitation spectrum, which comprises modified bulk modes and two different types of localized edge modes, explicit analytical expressions are obtained for the RKKY interaction for any two magnetic sites on the graphene ribbon. The results enable us to determine the RKKY contributions that arise individually from the bulk-like modes and from the two types of edge modes in the zigzag geometry. The importance of these contributions varies depending on the proximity of the magnetic impurities to each other and to an edge.

Full Text Available Fe3O4 is used as a catalyst in the Haber process and in the water gas shift reaction. In this work we have investigated the physical and chemical properties of Fe3O4@ Zigzag, @Armchair and @Chiral SWCNTs compare to Fe3O4@ -Cyclodextrin in view point of chemical reaction and sensitizes. The electrical properties such as NMR Shielding, electron densities, energy densities , potential energy densities, ELF, LOL, ellipticity of electron density , eta index and ECP for Fe3O4@ -Cyclodextrin shell and Fe3O4@ Zigzag, @Armchair and @Chiral SWCNTs have been calculated for the simulations. Our Calculation indicate that the Fe3O4 @ (7, 7 and Fe3O4 @ (10,5 and Fe3O4 @ (9, 0 have physical and chemical properties close to Fe3O4@ -Cyclodextrin and as well as the Fe3O4 @ (8,8 and Fe3O4 @ (11,6 and Fe3O4 @ (10, 0 are close to Fe3O4@ -Cyclodextrin.

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic Tn are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.

The approximate conservation of CP can be naturally understood if it arises as an automatic symmetry of the renormalizable Lagrangian. We present a specific realistic example with this feature. In this example, the global Peccei-Quinn symmetry and gauge symmetries of the model make the renormalizable Lagrangian CP invariant but allow non zero hierarchical masses and mixing among the three generations. The left-right and a horizontal U(1)_H symmetry is imposed to achieve this. The non-renormalizable interactions invariant under these symmetries violate CP whose magnitude can be in the experimentally required range if U(1)_H is broken at very high, typically, near the grand unification scale.

We study the phenomenology of supersymmetric flavor models. We show how the predictions of models based on spontaneously broken non-Abelian discrete flavor symmetries are altered when we include so-called Kaehler corrections. Furthermore, we discuss anomaly-free discrete R symmetries which are compatible with SU(5) unification. We find a set of symmetries compatible with suppressed Dirac neutrino masses and a unique symmetry consistent with the Weinberg operator. We also study a pseudo-anomalous U(1){sub R} symmetry which explains the fermion mass hierarchies and, when amended with additional singlet fields, ameliorates the fine-tuning problem.

Second-and third-order scalar ordinary differential equations of maximal symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in solutions and fundamental first integrals. The properties of the `exceptional symmetries’, i.e. those not considered to be generic to scalar equations of maximal symmetry, can be recast into a form which is applicable to all such equations of maximal symmetry. Some properties of these symmetries are demonstrated.

The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.

Full Text Available Some photographs of intensity of optical field of a photonic crystal fibre are presented in the contribution. Presented photographs document that the symmetry of photonic crystal creating the cladding of fibre is manifested in the symmetry of distribution of the optical field intensity. In case when more modes are excited in the fibre the symmetry of the generated field can be different as the symmetry of the eventual modes. How the symmetry may be changed is illustrated by amodel example.

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)×U(1) global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)×U(1) flavor symmetry breaking.

Full Text Available A number of studies have explored visual symmetry processing by measuring event related potentials and neural oscillatory activity. There is a sustained posterior negativity (SPN related to the presence of symmetry. There is also functional magnetic resonance imaging (MRI activity in extrastriate visual areas and in the lateral occipital complex. We summarise the evidence by answering six questions. (1 Is there an automatic and sustained response to symmetry in visual areas? Answer: Yes, and this suggests automatic processing of symmetry. (2 Which brain areas are involved in symmetry perception? Answer: There is an extended network from extrastriate areas to higher areas. (3 Is reflection special? Answer: Reflection is the optimal stimulus for a more general regularity-sensitive network. (4 Is the response to symmetry independent of view angle? Answer: When people classify patterns as symmetrical or random, the response to symmetry is view-invariant. When people attend to other dimensions, the network responds to residual regularity in the image. (5 How are brain rhythms in the two hemispheres altered during symmetry perception? Answer: Symmetry processing (rather than presence produces more alpha desynchronization in the right posterior regions. Finally, (6 does symmetry processing produce positive affect? Answer: Not in the strongest sense, but behavioural measures reveal implicit positive evaluation of abstract symmetry.

For the second harmonic generation (SHG) of a high-repetition rate and high pulse energy zigzag slab Nd:YAG laser, the direct bonding of two KTiPO4 (KTP) crystals is carried out and their characteristics are studied using the zigzag slab laser that produces 2.1 J energy pulses with a beam having a rectangular cross section at a pulse repetition rate of 100 Hz. Although an angle mismatch of four minutes between two tuning curves is observed for the bonded crystals, the energy conversion efficiency is the same as that of a single KTP crystal. The second harmonic produced is 1 J.

In this paper THD (Total Harmonic Distortion) is analysed and compared by using UPFC in a multi-line transmission system of 500 KV having 5-buses in two different arrangements. The UPFC converters are arranged as a Diode Clamped multilevel Converter (DCMLC) that leads to the cost reduction as compared with other multi-level converters. The comparison has been done by both series zig-zag/2Y-2Δ and series zig-zag/4Y transformer configuration for 48-pulses GTO based diode clamped converter. The ...

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content.

The group structure of the variant chiral symmetry discovered by Luscher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter subgroup, and the factor group whose elements are its cosets is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, non-commuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example - free overlap fermions - these non-canonical elements of lattice chiral symmetry are...

Wigner's little groups are subgroups of the Lorentz group dictating the internal space-time symmetries of massive and massless particles. These little groups are like O(3) and E(2) for massive and massless particles respectively. While the geometry of the O(3) symmetry is familiar to us, the geometry of the flat plane cannot explain the E(2)-like symmetry for massless particles. However, the geometry of a circular cylinder can explain the symmetry with the helicity and gauge degrees of freedom. It is shown further that the symmetry of the massless particle can be obtained as a zero-mass limit of O(3)-like symmetry for massive particles. It is shown further that the polarization of massless neutrinos is a consequence of gauge invariance, while the symmetry of massive neutrinos is still like O(3).

The study of hidden symmetries within Dirac's formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Faddeev-Jackiw approach, gauge and reparametrization symmetries are generated by the null eigenvectors of the sympletic matrix and not by constraints, suggesting the possibility of dealing systematically with hidden symmetries through this formalism. It is shown in this paper that indeed hidden symmetries of noninvariant or gauge fixed systems are equally well described by null eigenvectors of the sympletic matrix, just as the explicit invariances. The Faddeev-Jackiw approach therefore provide a systematic algorithm for treating all sorts of symmetries in an unified way. This technique is illustrated here by the SL(2,R) Kac-Moody current algebra of the 2-D induced gravity proposed by Polyakov, which is a hidden symmetry in the canonical approach of constrained systems via Dirac's method, after conformal and reparamet...

We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we present two models with the $SO(3)\\times U(1)$ global flavour symmetry in the lepton sector. After the flavour symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via see-saw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in...

Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.

that a nonprimitive, or centered, cell is obtained. In the triclinic system no symmetry restrictions occur, so a primitive cell can always be chosen. In...point (1/2, 1/2, 0) is a lattice point, and the unit cell defined by (1, 0, 0), (0, 1, 0), and (0, 0, 1) is not primitive. A primitive cell may be...in a primitive cell . The C centered unit cell has two lattice points in a plane shared by one other cell, in addition to the eight points at the

We present a new scenario for generating the baryon asymmetry of the Universe that is induced by a Nambu-Goldstone (NG) boson. The shift symmetry naturally controls the operators in the theory while allowing the NG boson to couple to the spacetime geometry as well as to the baryons. The cosmological background thus sources a coherent motion of the NG boson, which leads to baryogenesis. Good candidates of the baryon-generating NG boson are the QCD axion and axionlike fields. In these cases, the axion induces baryogenesis in the early Universe and can also serve as dark matter in the late Universe.

The subdivision graph $S(\\Sigma)$ of a graph $\\Sigma$ is obtained from $\\Sigma$ by `adding a vertex' in the middle of every edge of $\\Si$. Various symmetry properties of $\\S(\\Sigma)$ are studied. We prove that, for a connected graph $\\Sigma$, $S(\\Sigma)$ is locally $s$-arc transitive if and only if $\\Sigma$ is $\\lceil\\frac{s+1}{2}\\rceil$-arc transitive. The diameter of $S(\\Sigma)$ is $2d+\\delta$, where $\\Sigma$ has diameter $d$ and $0\\leqslant \\delta\\leqslant 2$, and local $s$-distance transi...

The conformal bootstrap program aims to catalog all conformal field theories (second-order phase transitions) in D dimensions. Despite its ambitious scope much progress has been made over the past decade, e.g. in computing critical exponents for the 3D O(N) models to high precision. At this stage, analytic methods to explore the CFT landscape are not as well developed. In this talk I will describe a new mathematical framework for the bootstrap known as "alpha space", which reduces crossing symmetry to a set of integral equations. Based on arXiv:1702.08471 (with Balt van Rees) and arXiv:1703.08159.

Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\\delta K^\\flat =0$ by using the Killing non-linear 1-form $K^\\flat$ and the spray operator $\\delta$ with the Finsler non-linear connection. $K^\\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\\delta K^\\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.

There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.

In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.

Full Text Available The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B–L-violating processes leads us to scrutinize the case of unbroken gauged B–L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g′, the Stückelberg mass MZ′, and the kinetic mixing angle χ. The new force could manifest itself at any scale, and we collect and derive bounds on g′ over the entire testable range MZ′=0–1013 eV, also of interest for the more popular case of spontaneously broken B–L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV

The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B-L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g', the Stueckelberg mass $M_{Z'}$, and the kinetic mixing angle $\\chi$. The new force could manifest itself at any scale, and we collect and derive bounds on g' over the entire testable range $M_{Z'}$ = 0 - $10^{13}$ eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV < $M_{Z'}$ < 10 GeV due to resonant enhancement of the rate $\\overline{f} f \\leftrightarrow \\overline{\

The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.

To understand the relation between the chiral symmetry breaking and monopoles, the chiral condensate which is the order parameter of the chiral symmetry breaking is calculated in the $\\overline{\\mbox{MS}}$ scheme at 2 [GeV]. First, we add one pair of monopoles, varying the monopole charges $m_{c}$ from zero to four, to SU(3) quenched configurations by a monopole creation operator. The low-lying eigenvalues of the Overlap Dirac operator are computed from the gauge links of the normal configurations and the configurations with additional monopoles. Next, we compare the distributions of the nearest-neighbor spacing of the low-lying eigenvalues with the prediction of the random matrix theory. The low-lying eigenvalues not depending on the scale parameter $\\Sigma$ are compared to the prediction of the random matrix theory. The results show the consistency with the random matrix theory. Thus, the additional monopoles do not affect the low-lying eigenvalues. Moreover, we discover that the additional monopoles increa...

We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings in d-dimensional Euclidean space {{{R}}d} . Specifically, we ascertain statistics of the densities and kissing numbers as well as the numbers of distinct symmetries of the packings for dimensions 8 through 13 using the stochastic Voronoi algorithm. The extreme lattices in a fixed dimension of space d (d≥slant 8 ) are dominated by typical lattices that have similar packing properties, such as packing densities and kissing numbers, while the best and the worst packers are in the long tails of the distribution of the extreme lattices. We also study the validity of the recently proposed decorrelation principle, which has important implications for sphere packings in general. The degree to which extreme-lattice packings decorrelate as well as how decorrelation is related to the packing density and symmetry of the lattices as the space dimension increases is also investigated. We find that the extreme lattices decorrelate with increasing dimension, while the least symmetric lattices decorrelate faster.

In this effort, we report on development of specific sensors dedicated for detection of two of these volatiles, namely ethanol and acetone, below the prescribed statutory limits. Single crystalline Al-doped SnO2 zigzag nanobelt structures were deposited on Si substrate by a catalyst-free thermal evaporation method. The Al-doped SnO2 zigzag nanostructures exhibit high sensitivity and repeatability together with coveted features like fast response and excellent stability. Structural attributes involving the crystal quality and morphology of Al-doped SnO2 zigzag nanobelts were analyzed using X-ray photoelectron spectroscopy (XPS), scanning electron microscopy and transmission electron microscopy. The microscopic images revealed formation of randomly oriented 'zigzag-like' nanobelts with characteristic width between 60 nm and 200 nm and length of 50-300 μm. The Al-doping was observed to have a discerning effect in enhancing the sensitivity in comparison to the pristine nanowires by creating excess oxygen vacancies in the crystal lattice, confirmed through XPS and PL spectra.

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.

We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines the square roots of the kinetic and potential energies and connects solutions of the same dynamical problem (the potential is an invariant function). The other symmetry connects solutions of different dynamical problems (the potential is a scalar function). The existence of corresponding conserved quantities is examined using Noethers theorem and it is shown that the invariant-potential symmetry is correlated with energy conservation. In the Hamilton-Jacobi picture the invariant-potential transformation provides an example of a field-dependent symmetry in point mechanics. It is shown that this transformation is not a symmetry of the Schroedinger equation.

This work originates from a first year undergraduate research project on hidden symmetries of the dynamics for classical Hamiltonian systems, under the program 'Jovens talentos para a Ciencia' of Brazilian funding agency Capes. For pedagogical reasons the main subject chosen was Kepler's problem of motion under a central potential, since it is a completely solved system. It is well known that for this problem the group of dynamical symmetries is strictly larger than the isometry group O(3), the extra symmetries corresponding to hidden symmetries of the dynamics. By taking the point of view of examining the group action of the dynamical symmetries on the allowed trajectories, it is possible to teach in the same project basic elements of as many important subjects in physics as: Hamiltonian formalism, hidden symmetries, integrable systems, group theory, and the use of manifolds.

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non--Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.

In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of dual-BRST symmetry in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent of BRST symmetries. We show that the BRST and co-BRST symmetries are independent symmetries in the same fashion as the exterior and co-exterior derivatives are independent entities belonging to the set of de Rham cohomological operators of differential geometry.

We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such "indirect" models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify large classes of suitable discrete family symmetries, namely the $\\Delta(3n^2)$ and $\\Delta(6n^2)$ groups, together with other examples such as $Z_7\\rtimes Z_3$. In such indirect models the implementation of the type I see-saw mechanism is straightforward using constrained sequential dominance. However the accidental neutrino flavour symmetry may be easily violated, for example leading to a large reactor angle, while maintaining accurately the tri-bimaximal solar and atmospheric predictions.

Nanoribbons are quasi one-dimensional structures which have interesting electronic properties on the basis of their edge geometries, and width. We studied the electronic properties of hydrogen and fluorine-terminated zigzag BNC nanoribbons (BNCNRs) using a first-principles based density functional theory approach. We considered BNCNRs that were composed of an equal number of C-C and B-N dimers; one of the edges ends with an N atom and opposite edge ends with a C atom. These two edge atoms are passivated by H or F atoms. Our results suggest that hydrogen-terminated BNCNRs (H-BNCNRs) and flourine-terminated BNCNRs (F-BNCNRs) have different electronic properties. H-BNCNRs exhibit intrinsic half-metallic behavior while F-BNCNRs are indirect band gap semiconductors. Chemical functionalization of BNCNRs with H and F atoms show that BNCNRs have a diverse range of electronic properties.

Electronic properties of single-walled boron nitride nanotube in zig-zag form are numerically investigated by replacing B atoms with C atoms. Using a tight-binding Hamiltonian, the methods based on Green’s function theory, Landauer formalism and Dyson equation, the electronic density of states and electronic conductance in boron nitride nanotube and boron carbonitride nanotube are calculated. Our calculations indicate that in a boron nitride nanotube, the localized states associated with C impurities appear as the concentration of C atoms increases. The boron carbonitride nanotube thus behaves like a semiconductor. Also, by increasing the C atom concentration, the voltage in the ﬁrst step on the – characteristics decreases, whereas the corresponding current increases.

We study spin transport in a zigzag graphene nanoribbon sample with two ferromagnetic strips deposited on the two sides of the ribbon.A tight-binding Hamiltonian was adopted to describe the sample connected to two one-dimensional leads.Our theoretical study shows that the resonance peaks of conductance for the spin-up and spin-down electrons are separated for the parallel configuration of the ferromagnetic strips,while they are not separated for the case of antiparallel configuration.This means that giant magnetoresistance can be produced at particular energies by altering the configurations of the ferromagnetic strips,and the device can be designed as a spin filter.

Full Text Available Abstract Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers or rotational symmetry (e.g. sea urchins and many flowers. So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.

Discrete Abelian symmetries (ZN) are a common “artifact” of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U(1) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the ...

Full Text Available This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown.

In the context of the relationship between physics of cosmological dark matter and symmetry of elementary particles, a wide list of dark matter candidates is possible. New symmetries provide stability of different new particles and their combination can lead to a multicomponent dark matter. The pattern of symmetry breaking involves phase transitions in the very early Universe, extending the list of candidates by topological defects and even primordial nonlinear structures.

We present rules for determining the number of physical parameters in models with exact flavor symmetries. In such models the total number of parameters (physical and unphysical) needed to described a matrix is less than in a model without the symmetries. Several toy examples are studied in order to demonstrate the rules. The use of global symmetries in studying the minimally supersymmetric standard model (MSSM) is examined.

Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.

We identify the symmetry underlying the recently observed spectral-parameter transformations of holographic Wilson loops alias minimal surfaces in AdS/CFT. The generator of this nonlocal symmetry is shown to furnish a raising operator on the classical Yangian-type charges of symmetric coset models. We explicitly demonstrate how this master symmetry acts on strong-coupling Wilson loops and indicate a possible extension to arbitrary coupling.

Based on the total time derivative along the trajectory of the time, we study the unified symmetry of Vacco dynamical systems. The definition and the criterion of the unified symmetry for the system are given. Three kinds of conserved quantities, i.e. the Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity, are deduced from the unified symmetry. An example is presented to illustrate the results.

The grounds on which the nuclear pseudospin symmetry (PSS) is supposed to be based are analysed within the relativistic mean-field framework. A comparative analysis of the mechanisms responsible for the breaking of the spin and pseudospin symmetries, which clarifies the different nature of these symmetries, is made. A non-relativistic explanation of the PSS, based on the effect of the spin-orbit interaction, is also sketched.